Daily Papers

Jailbreak attacks reveal a persistent weakness in aligned Large Language Models: carefully crafted prompts can elicit policy-violating responses despite safety training. While most defenses operate at the prompt or output level, it remains unclear how harmful intent is encoded within the model's internal representations. We investigate this question by analyzing token-level predictive entropy trajectories across layers of a frozen LLM using the logit lens. We find that static aggregate statistics of prompt-level entropy (e.g., mean, variance) carry little discriminative signal, whereas features capturing how entropy evolves across token positions, such as monotonic rank-based trend scores, are substantially more informative. Importantly, this signal is not uniform across model depth: it is concentrated in intermediate layers and degrades at the final layer, indicating that jailbreak-relevant structure is most pronounced in mid-network representations rather than at the output head. Across multiple models (Llama, Qwen, Gemma) and adversarial benchmarks, these entropy dynamics provide architecture-consistent separation without additional training. Together, our findings show that jailbreak behavior is reflected in structured intermediate uncertainty dynamics, clarifying both which entropy-derived features encode harmful intent and where in the network that signal is most pronounced.

Hybrid training methods for large language models combine supervised fine tuning (SFT) on expert demonstrations with reinforcement learning (RL) on model rollouts, typically at the sample level. We propose Entropy Gated Selective Policy Optimization (EGSPO), a three stage framework that extends sample level mixing with token level gradient modulation. Stage 1, SFT expert learning, establishes a reliable warm up policy using expert demonstrations with a pure SFT loss. Stage 2, RL rollout generation, samples trajectories from the current policy and computes per token predictive entropy. Stage 3, the EGSPO mechanism, applies entropy gated gradient allocation: a predictive entropy module routes high entropy tokens to full PPO updates to encourage exploration, and low entropy tokens to attenuated PPO updates to reduce variance and preserve knowledge. Critically, both branches incorporate the advantage function A_t, ensuring that incorrect trajectories receive consistent negative learning signals and preventing reinforcement of confident errors. EGSPO achieves consistent improvements on mathematical reasoning benchmarks, with gains of 3.8 percent on AIME and 2.9 percent on MATH over the CHORD phi baseline, while incurring only 3.4 percent additional computational overhead.

Reinforcement learning (RL) has shown strong potential for enhancing reasoning in multimodal large language models, yet existing video reasoning methods often rely on coarse sequence-level rewards or single-factor token selection, neglecting fine-grained links among visual inputs, temporal dynamics, and linguistic outputs, limiting both accuracy and interpretability. We propose Video-KTR, a modality-aware policy shaping framework that performs selective, token-level RL by combining three attribution signals: (1) visual-aware tokens identified via counterfactual masking to reveal perceptual dependence; (2) temporal-aware tokens detected through frame shuffling to expose temporal sensitivity; and (3) high-entropy tokens signaling predictive uncertainty. By reinforcing only these key tokens, Video-KTR focuses learning on semantically informative, modality-sensitive content while filtering out low-value tokens. Across five challenging benchmarks, Video-KTR achieves state-of-the-art or highly competitive results, achieving 42.7\% on Video-Holmes (surpassing GPT-4o) with consistent gains on both reasoning and general video understanding tasks. Ablation studies verify the complementary roles of the attribution signals and the robustness of targeted token-level updates. Overall, Video-KTR improves accuracy and interpretability, offering a simple, drop-in extension to RL for complex video reasoning. Our code and models are available at https://github.com/zywang0104/Video-KTR.

Uncertainty Quantification (UQ) research has primarily focused on closed-book factual question answering (QA), while contextual QA remains unexplored, despite its importance in real-world applications. In this work, we focus on UQ for the contextual QA task and propose a theoretically grounded approach to quantify epistemic uncertainty. We begin by introducing a task-agnostic, token-level uncertainty measure defined as the cross-entropy between the predictive distribution of the given model and the unknown true distribution. By decomposing this measure, we isolate the epistemic component and approximate the true distribution by a perfectly prompted, idealized model. We then derive an upper bound for epistemic uncertainty and show that it can be interpreted as semantic feature gaps in the given model's hidden representations relative to the ideal model. We further apply this generic framework to the contextual QA task and hypothesize that three features approximate this gap: context-reliance (using the provided context rather than parametric knowledge), context comprehension (extracting relevant information from context), and honesty (avoiding intentional lies). Using a top-down interpretability approach, we extract these features by using only a small number of labeled samples and ensemble them to form a robust uncertainty score. Experiments on multiple QA benchmarks in both in-distribution and out-of-distribution settings show that our method substantially outperforms state-of-the-art unsupervised (sampling-free and sampling-based) and supervised UQ methods, achieving up to a 13-point PRR improvement while incurring a negligible inference overhead.

Unlearning in large language models (LLMs) has emerged as a promising safeguard against adversarial behaviors. When the forgetting loss is applied uniformly without considering token-level semantic importance, model utility can be unnecessarily degraded. Recent studies have explored token-wise loss regularizers that prioritize informative tokens, but largely rely on ground-truth confidence or external linguistic parsers, which limits their ability to capture contextual information or the model's overall predictive state. Intuitively, function words like "the" primarily serve syntactic roles and are highly predictable with little ambiguity, but informative words admit multiple plausible alternatives with greater uncertainty. Based on this intuition, we propose Entropy-guided Token Weighting (ETW), a token-level unlearning regularizer that uses entropy of the predictive distribution as a proxy for token informativeness. We demonstrate that informative tokens tend to have higher entropy, whereas structural tokens tend to have lower entropy. This behavior enables ETW to achieve more effective unlearning while better preserving model utility than existing token-level approaches.

In large language models (LLMs), each block operates on the residual stream to map input token sequences to output token distributions. However, most of the interpretability literature focuses on internal latent representations, leaving token-space dynamics underexplored. The high dimensionality and categoricity of token distributions hinder their analysis, as standard statistical descriptors are not suitable. We show that the entropy of logit-lens predictions overcomes these issues. In doing so, it provides a per-layer scalar, permutation-invariant metric. We introduce Entropy-Lens to distill the token-space dynamics of the residual stream into a low-dimensional signal. We call this signal the entropy profile. We apply our method to a variety of model sizes and families, showing that (i) entropy profiles uncover token prediction dynamics driven by expansion and pruning strategies; (ii) these dynamics are family-specific and invariant under depth rescaling; (iii) they are characteristic of task type and output format; (iv) these strategies have unequal impact on downstream performance, with the expansion strategy usually being more critical. Ultimately, our findings further enhance our understanding of the residual stream, enabling a granular assessment of how information is processed across model depth.

Reinforcement-learning-based post-training has become a key approach for improving the reasoning ability of large language models, but its token-level learning signals remain poorly understood. This work studies their heterogeneity through attention entropy, which measures how concentrated or diffuse the contextual support is for each response token. We first show that token-level RL objectives are sparsely estimable: uniformly random 20 percent token subsets preserve much of the full-token held-out performance, suggesting substantial redundancy in token-level updates. However, entropy-structured subsets behave very differently. Low-attention-entropy tokens, which we call anchors, rely on concentrated support, produce stable gradients aligned with full-token updates, and provide a reliable optimization backbone, but tend to plateau on harder benchmarks. High-attention-entropy tokens, which we call explorers, aggregate more diffuse context and induce larger but more volatile gradients. Explorer-only training is unstable on average, though rare successful runs suggest that these tokens may contain useful hard-reasoning signals when optimization remains stable. We support this anchor-explorer spectrum with evidence-gathering analyses, entropy dynamics, gradient-geometry diagnostics, and controls showing that position, predictive entropy, and loss normalization do not explain the observed asymmetry. Finally, a dynamic entropy-aware soft-reweighting intervention improves Qwen3-8B-Base from 34.39 to 37.40 held-out average in the strongest setting. These findings suggest that attention entropy reveals optimization-relevant structure in token-level RL signals, and that uniform token averaging can obscure meaningful heterogeneity in reasoning post-training.

Large language model (LLM) tokenizers act as structured compressors: by mapping text to discrete token sequences, they determine token count (and thus compute and context usage) and the statistical structure seen by downstream models. Despite their central role in LLM pipelines, the link between tokenization, compression efficiency and induced structure is not well understood. We empirically demonstrate that tokenizer training scale redistributes entropy: as training data grows, the token stream becomes more diverse in aggregate (higher unigram entropy) yet markedly more predictable in-context (lower higher-order conditional entropies), indicating that tokenization absorbs substantial short-range regularity although these gains degrade under train-test domain mismatch. To ground these observations, we first benchmark i) pretrained GPT-family tokenizers as black-box compressors across various domains, and ii) learned tokenizers across configurations spanning vocabulary size, training scale, and domain. Next, we study tokenization as a transform for universal compression and introduce a compression-aware BPE variant. Finally, we adopt a channel lens and introduce capacity-utilization metrics to analyze tokenizer behaviour and outline implications for downstream modeling. Put together, our results expose various trade-offs between compression, induced structure, and robustness under domain shift, and motivate principled, compression-aware tokenizer design.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

Uncertainty quantification (UQ) for open-ended language generation remains a critical yet underexplored challenge, especially under black-box constraints where internal model signals are inaccessible. In this paper, we introduce Token-Entropy Conformal Prediction (TECP), a novel framework that leverages token-level entropy as a logit-free, reference-free uncertainty measure and integrates it into a split conformal prediction (CP) pipeline to construct prediction sets with formal coverage guarantees. Unlike existing approaches that rely on semantic consistency heuristics or white-box features, TECP directly estimates epistemic uncertainty from the token entropy structure of sampled generations and calibrates uncertainty thresholds via CP quantiles to ensure provable error control. Empirical evaluations across six large language models and two benchmarks (CoQA and TriviaQA) demonstrate that TECP consistently achieves reliable coverage and compact prediction sets, outperforming prior self-consistency-based UQ methods. Our method provides a principled and efficient solution for trustworthy generation in black-box LLM settings.

Most unified large multimodal models (LMMs) that support both visual understanding and image generation still rely on curated post-training supervision, such as human annotations, preference labels, or external reward models. We ask whether a unified LMM can improve both abilities autonomously using only unlabeled images. We propose a self-evolving training framework with three internal roles: a Proposer that generates visual questions, a Solver that answers and evaluates them, and a Generator that synthesizes images. Training uses only self-derived consistency signals, without human annotations, preference labels, or task-trained external reward/judge models. To stabilize learning, we introduce Solver Token Entropy (STE), a continuous difficulty signal based on token-level prediction uncertainty that remains useful even when sample-level consistency becomes unreliable. For image generation, we design a multi-scale internal evaluation scheme that combines question-answer fidelity scoring with cycle-consistent captioning. This creates a solver-mediated coupling, where better visual understanding enables more reliable generation assessment and stronger internal training signals. The framework preserves the same role decomposition, reward logic, and training schedule across diffusion-based BLIP3o, rectified-flow BAGEL, and autoregressive VARGPT-v1.1 architectures, requiring only each backbone's native prompting and generation interface. Across eight understanding metrics, our method consistently improves over the corresponding base models. On BAGEL, it achieves a +3.5% absolute gain on MMMU and improves GenEval image generation performance from 82% to 85%. Code and models are publicly released.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

We provide new estimates of an asymptotic upper bound on the entropy of English using the large language model LLaMA-7B as a predictor for the next token given a window of past tokens. This estimate is significantly smaller than currently available estimates in cover1978convergent, lutati2023focus. A natural byproduct is an algorithm for lossless compression of English text which combines the prediction from the large language model with a lossless compression scheme. Preliminary results from limited experiments suggest that our scheme outperforms state-of-the-art text compression schemes such as BSC, ZPAQ, and paq8h.

This paper focuses on task-agnostic prompt compression for better generalizability and efficiency. Considering the redundancy in natural language, existing approaches compress prompts by removing tokens or lexical units according to their information entropy obtained from a causal language model such as LLaMa-7B. The challenge is that information entropy may be a suboptimal compression metric: (i) it only leverages unidirectional context and may fail to capture all essential information needed for prompt compression; (ii) it is not aligned with the prompt compression objective. To address these issues, we propose a data distillation procedure to derive knowledge from an LLM to compress prompts without losing crucial information, and meantime, introduce an extractive text compression dataset. We formulate prompt compression as a token classification problem to guarantee the faithfulness of the compressed prompt to the original one, and use a Transformer encoder as the base architecture to capture all essential information for prompt compression from the full bidirectional context. Our approach leads to lower latency by explicitly learning the compression objective with smaller models such as XLM-RoBERTa-large and mBERT. We evaluate our method on both in-domain and out-of-domain datasets, including MeetingBank, LongBench, ZeroScrolls, GSM8K, and BBH. Despite its small size, our model shows significant performance gains over strong baselines and demonstrates robust generalization ability across different LLMs. Additionally, our model is 3x-6x faster than existing prompt compression methods, while accelerating the end-to-end latency by 1.6x-2.9x with compression ratios of 2x-5x.

Multimodal large language models (MLLMs) incur substantial inference cost due to the processing of hundreds of visual tokens per image. Although token pruning has proven effective for accelerating inference, determining when and where to prune remains largely heuristic. Existing approaches typically rely on static, empirically selected layers, which limit interpretability and transferability across models. In this work, we introduce a matrix-entropy perspective and identify an "Entropy Collapse Layer" (ECL), where the information content of visual representations exhibits a sharp and consistent drop, which provides a principled criterion for selecting the pruning stage. Building on this observation, we propose EntropyPrune, a novel matrix-entropy-guided token pruning framework that quantifies the information value of individual visual tokens and prunes redundant ones without relying on attention maps. Moreover, to enable efficient computation, we exploit the spectral equivalence of dual Gram matrices, reducing the complexity of entropy computation and yielding up to a 64x theoretical speedup. Extensive experiments on diverse multimodal benchmarks demonstrate that EntropyPrune consistently outperforms state-of-the-art pruning methods in both accuracy and efficiency. On LLaVA-1.5-7B, our method achieves a 68.2% reduction in FLOPs while preserving 96.0% of the original performance. Furthermore, EntropyPrune generalizes effectively to high-resolution and video-based models, highlighting the strong robustness and scalability in practical MLLM acceleration. The code will be publicly available at https://github.com/YahongWang1/EntropyPrune.

Hallucination in large language models (LLMs) can be detected by assessing the uncertainty of model outputs, typically measured using entropy. Semantic entropy (SE) enhances traditional entropy estimation by quantifying uncertainty at the semantic cluster level. However, as modern LLMs generate longer one-sentence responses, SE becomes less effective because it overlooks two crucial factors: intra-cluster similarity (the spread within a cluster) and inter-cluster similarity (the distance between clusters). To address these limitations, we propose a simple black-box uncertainty quantification method inspired by nearest neighbor estimates of entropy. Our approach can also be easily extended to white-box settings by incorporating token probabilities. Additionally, we provide theoretical results showing that our method generalizes semantic entropy. Extensive empirical results demonstrate its effectiveness compared to semantic entropy across two recent LLMs (Phi3 and Llama3) and three common text generation tasks: question answering, text summarization, and machine translation. Our code is available at https://github.com/BigML-CS-UCLA/SNNE.

Speculative decoding (SD) accelerates large language model (LLM) reasoning by using a small draft model to generate candidate tokens, which the target LLM either accepts directly or regenerates upon rejection. However, excessive alignment between the draft and target models constrains SD to the performance of the target LLM. To address this limitation, we propose Entropy-Aware Speculative Decoding (EASD), a training-free enhancement. Building on standard SD, EASD incorporates a dynamic entropy-based penalty. At each decoding step, we employ the entropy of the sampling distribution to quantify model uncertainty. When both models exhibit high entropy with substantial overlap among their top-N predictions, the corresponding token is rejected and re-sampled by the target LLM. This penalty prevents low-confidence errors from propagating. By incorporating draft-model verification, EASD enables the possibility of surpassing the target model's inherent performance. Experiments across multiple reasoning benchmarks demonstrate that EASD consistently outperforms existing SD methods and, in most cases, surpasses the target LLM itself. We further prove that the efficiency of EASD is comparable to that of SD. The code can be found in the Supplementary Materials.

We introduce a simple, yet novel entropy-based framework to drive token efficiency in large language models during reasoning tasks. Our approach uses Shannon entropy from token-level logprobs as a confidence signal to enable early stopping, achieving 25-50% computational savings while maintaining task accuracy. Crucially, we demonstrate that entropy-based confidence calibration represents an emergent property of advanced post-training optimization present in modern reasoning models but notably absent in standard instruction-tuned and pre-trained models (Llama 3.3 70B). We show that the entropy threshold to stop reasoning varies from model to model but can be calculated easily in one shot using only a few examples from existing reasoning datasets. Our results indicate that advanced reasoning models often know that they've gotten a correct answer early on, and that this emergent confidence awareness can be exploited to save tokens and reduce latency. The framework demonstrates consistent performance across reasoning-optimized model families with 25-50% computational cost reduction while preserving accuracy, revealing that confidence mechanisms represent a distinguishing characteristic of modern post-trained reasoning systems versus their predecessors.

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Despite their widespread use, the mechanisms by which large language models (LLMs) represent and regulate uncertainty in next-token predictions remain largely unexplored. This study investigates two critical components believed to influence this uncertainty: the recently discovered entropy neurons and a new set of components that we term token frequency neurons. Entropy neurons are characterized by an unusually high weight norm and influence the final layer normalization (LayerNorm) scale to effectively scale down the logits. Our work shows that entropy neurons operate by writing onto an unembedding null space, allowing them to impact the residual stream norm with minimal direct effect on the logits themselves. We observe the presence of entropy neurons across a range of models, up to 7 billion parameters. On the other hand, token frequency neurons, which we discover and describe here for the first time, boost or suppress each token's logit proportionally to its log frequency, thereby shifting the output distribution towards or away from the unigram distribution. Finally, we present a detailed case study where entropy neurons actively manage confidence in the setting of induction, i.e. detecting and continuing repeated subsequences.

Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects intrinsic uncertainty induced by the pre-training prior. Ignoring entropy can misidentify noisy or easily replaceable tokens as learning-critical, while ignoring probability fails to reflect target-specific alignment. RankTuner introduces a probability--entropy calibration signal, the Relative Rank Indicator, which compares the rank of the ground-truth token with its expected rank under the prediction distribution. The inverse indicator is used as a token-wise Relative Scale to reweight the fine-tuning objective, focusing updates on truly under-learned tokens without over-penalizing intrinsically uncertain positions. Experiments on multiple backbones show consistent improvements on mathematical reasoning benchmarks, transfer gains on out-of-distribution reasoning, and pre code generation performance over probability-only or entropy-only reweighting baselines.

Many commercial Large Language Models (LLMs) are often closed-source, limiting developers to prompt tuning for aligning content generation with specific applications. While these models currently do not provide access to token logits, we argue that if such access were available, it would enable more powerful adaptation techniques beyond prompt engineering. In this paper, we propose a token-level probability reweighting framework that, given access to logits and a small amount of task-specific data, can effectively steer black-box LLMs toward application-specific content generation. Our approach views next-token prediction through the lens of supervised classification. We show that aligning black-box LLMs with task-specific data can be formulated as a label noise correction problem, leading to Plugin model -- an autoregressive probability reweighting model that operates solely on logits. We provide theoretical justification for why reweighting logits alone is sufficient for task adaptation. Extensive experiments with multiple datasets, LLMs, and reweighting models demonstrate the effectiveness of our method, advocating for broader access to token logits in closed-source models.

With the development of large language models (LLMs), efficient inference through Key-Value (KV) cache compression has attracted considerable attention, especially for long-context generation. To compress the KV cache, recent methods identify critical KV tokens through heuristic ranking with attention scores. However, these methods often struggle to accurately determine critical tokens as they neglect the temporal patterns in attention scores, resulting in a noticeable degradation in LLM performance. To address this challenge, we propose AttentionPredictor, which is the first learning-based critical token identification approach. Specifically, AttentionPredictor learns a lightweight convolution model to capture spatiotemporal patterns and predict the next-token attention score. An appealing feature of AttentionPredictor is that it accurately predicts the attention score while consuming negligible memory. Moreover, we propose a cross-token critical cache prefetching framework that hides the token estimation time overhead to accelerate the decoding stage. By retaining most of the attention information, AttentionPredictor achieves 16times KV cache compression with comparable LLM performance, significantly outperforming the state-of-the-art.

Machine unlearning has emerged as a critical capability for addressing privacy, safety, and regulatory concerns in large language models (LLMs). Existing methods operate at the sequence level, applying uniform updates across all tokens despite only a subset encoding the knowledge targeted for removal. This introduces gradient noise, degrades utility, and leads to suboptimal forgetting. We propose TokenUnlearn, a token-level attribution framework that identifies and selectively targets critical tokens. Our approach combines knowledge-aware signals via masking, and entropy-aware signals to yield importance scores for precise token selection. We develop two complementary strategies: hard selection, applying unlearning only to high-importance tokens, and soft weighting, modulating gradient contributions based on importance scores. Both extend existing methods to token-level variants. Theoretical analysis shows token-level selection improves gradient signal-to-noise ratio. Experiments on TOFU and WMDP benchmarks across three model architectures demonstrate consistent improvements over sequence-level baselines in both forgetting effectiveness and utility preservation.

Recent works have argued that high-level semantic concepts are encoded "linearly" in the representation space of large language models. In this work, we study the origins of such linear representations. To that end, we introduce a simple latent variable model to abstract and formalize the concept dynamics of the next token prediction. We use this formalism to show that the next token prediction objective (softmax with cross-entropy) and the implicit bias of gradient descent together promote the linear representation of concepts. Experiments show that linear representations emerge when learning from data matching the latent variable model, confirming that this simple structure already suffices to yield linear representations. We additionally confirm some predictions of the theory using the LLaMA-2 large language model, giving evidence that the simplified model yields generalizable insights.

State-of-the-art language models are autoregressive and operate on subword units known as tokens. Specifically, one must encode the conditioning string into a list of tokens before passing to the language models for next-token prediction. We show that popular encoding schemes, such as maximum prefix encoding (MPE) and byte-pair-encoding (BPE), induce a sampling bias that cannot be mitigated with more training or data. To counter this universal problem, for each encoding scheme above, we propose a novel algorithm to obtain unbiased estimates from any language model trained on tokenized data. Our methods do not require finetuning the model, and the complexity, defined as the number of model runs, scales linearly with the sequence length in the case of MPE. As a result, we show that one can simulate token-free behavior from a tokenized language model. We empirically verify the correctness of our method through a Markov-chain setup, where it accurately recovers the transition probabilities, as opposed to the conventional method of directly prompting tokens into the language model.

We study the fractal structure of language, aiming to provide a precise formalism for quantifying properties that may have been previously suspected but not formally shown. We establish that language is: (1) self-similar, exhibiting complexities at all levels of granularity, with no particular characteristic context length, and (2) long-range dependent (LRD), with a Hurst parameter of approximately H=0.70. Based on these findings, we argue that short-term patterns/dependencies in language, such as in paragraphs, mirror the patterns/dependencies over larger scopes, like entire documents. This may shed some light on how next-token prediction can lead to a comprehension of the structure of text at multiple levels of granularity, from words and clauses to broader contexts and intents. We also demonstrate that fractal parameters improve upon perplexity-based bits-per-byte (BPB) in predicting downstream performance. We hope these findings offer a fresh perspective on language and the mechanisms underlying the success of LLMs.

As large language models continue to scale, their growing computational and storage demands pose significant challenges for real-world deployment. In this work, we investigate redundancy within Transformer-based models and propose an entropy-based pruning strategy to enhance efficiency while maintaining performance. Empirical analysis reveals that the entropy of hidden representations decreases in the early blocks but progressively increases across most subsequent blocks. This trend suggests that entropy serves as a more effective measure of information richness within computation blocks. Unlike cosine similarity, which primarily captures geometric relationships, entropy directly quantifies uncertainty and information content, making it a more reliable criterion for pruning. Extensive experiments demonstrate that our entropy-based pruning approach surpasses cosine similarity-based methods in reducing model size while preserving accuracy, offering a promising direction for efficient model deployment.

We present Entropy Adaptive Decoding (EAD), a novel approach for efficient language model inference that dynamically switches between different-sized models based on prediction uncertainty. By monitoring rolling entropy in model logit distributions, our method identifies text regions where a smaller model suffices and switches to a larger model only when prediction uncertainty exceeds a threshold. Unlike speculative decoding approaches that maintain perfect output fidelity through verification, EAD accepts controlled output divergence in exchange for computational efficiency. Our experiments on the MATH benchmark demonstrate remarkable efficiency gains across different model families. Using the LLaMA family, we maintain 96.7\% of the 11B model's performance (50.4\% vs 52.1\%) while using it for only 43\% of tokens, decreasing computational cost by 41.5\%. These gains become more pronounced with larger size differentials in the Qwen family, where we achieve 92.9\% of the 14B model's performance (74.3\% vs 80.0\%) while using it for just 25\% of tokens, decreasing computational cost by 67\%. The consistency of these results across model pairs suggests that language model computation can be significantly optimized by selectively deploying model capacity based on local generation complexity. Our findings indicate that current approaches to model inference may be unnecessarily conservative in their pursuit of perfect output fidelity, and that accepting minor performance trade-offs can enable dramatic reductions in computational costs.

Multimodal reward models are crucial for aligning multimodal large language models with human preferences. Recent works have incorporated reasoning capabilities into these models, achieving promising results. However, training these models suffers from two critical challenges: (1) the inherent noise in preference datasets, which degrades model performance, and (2) the inefficiency of conventional training methods, which ignore the differences in sample difficulty. In this paper, we identify a strong correlation between response entropy and accuracy, indicating that entropy can serve as a reliable and unsupervised proxy for annotation noise and sample difficulty. Based on this insight, we propose a novel Entropy-Guided Training (EGT) approach for multimodal reasoning reward models, which combines two strategies: (1) entropy-guided data curation to mitigate the impact of unreliable samples, and (2) an entropy-guided training strategy that progressively introduces more complex examples. Extensive experiments across three benchmarks show that the EGT-trained model consistently outperforms state-of-the-art multimodal reward models.

Unlearning in Multimodal Large Language Models (MLLMs) prevents the model from revealing private information when queried about target images. Existing MLLM unlearning methods largely adopt approaches developed for LLMs. They treat all answer tokens uniformly, disregarding their varying importance in the unlearning process. Moreover, these methods focus exclusively on the language modality, disregarding visual cues that indicate key tokens in answers. In this paper, after formulating the problem of unlearning in multimodal question answering for MLLMs, we propose Visual-Guided Key-Token Regularization (ViKeR). We leverage irrelevant visual inputs to predict ideal post-unlearning token-level distributions and use these distributions to regularize the unlearning process, thereby prioritizing key tokens. Further, we define key tokens in unlearning via information entropy and discuss ViKeR's effectiveness through token-level gradient reweighting, which amplifies updates on key tokens. Experiments on MLLMU and CLEAR benchmarks demonstrate that our method effectively performs unlearning while mitigating forgetting and maintaining response coherence.

Agentic language model (LM) systems power modern applications like "Deep Research" and "Claude Code," and leverage multi-LM architectures to overcome context limitations. Beneath their apparent diversity lies a recurring pattern: smaller "compressor" LMs (that can even run locally) distill raw context into compact text that is then consumed by larger "predictor" LMs. Despite their popularity, the design of compressor-predictor systems remains largely ad hoc, with little guidance on how compressor and predictor choices shape downstream performance. In practice, attributing gains to compression versus prediction requires costly, task-specific pairwise sweeps. We argue that these agentic system design questions are, at root, information-theoretic. Viewing the compressor LM as a noisy channel, we introduce a simple estimator of mutual information between the context and its compression to quantify compression quality in a task-independent way. We show that mutual information strongly predicts downstream performance, independent of any specific task. Through an information-theoretic framework, we perform a comprehensive empirical analysis across five datasets and three model families. Results reveal that larger compressors not only are more accurate, but also more token-efficient, conveying more bits of information per token. A 7B Qwen-2.5 compressor, for instance, is 1.6times more accurate, 4.6times more concise, and conveys 5.5times more bits of mutual information per token than its 1.5B sibling. Across datasets, scaling compressors is substantially more effective than scaling predictors, enabling larger on-device compressors to pair with smaller cloud predictors. Applied to a Deep Research system, these principles enable local compressors as small as 3B parameters to recover 99% of frontier-LM accuracy at 26% of API costs.

State-of-the-art language generation models can degenerate when applied to open-ended generation problems such as text completion, story generation, or dialog modeling. This degeneration usually shows up in the form of incoherence, lack of vocabulary diversity, and self-repetition or copying from the context. In this paper, we postulate that ``human-like'' generations usually lie in a narrow and nearly flat entropy band, and violation of these entropy bounds correlates with degenerate behavior. Our experiments show that this stable narrow entropy zone exists across models, tasks, and domains and confirm the hypothesis that violations of this zone correlate with degeneration. We then use this insight to propose an entropy-aware decoding algorithm that respects these entropy bounds resulting in less degenerate, more contextual, and "human-like" language generation in open-ended text generation settings.

Recent dynamic tokenisation methods operate directly on bytes and pool their latent representations into patches. This bears similarities to computational models of word segmentation that determine lexical boundaries using spikes in an autoregressive model's prediction error. Inspired by this connection, we explore whether grouping predictable bytes - rather than pooling their representations - can yield a useful fixed subword vocabulary. We propose a new information-driven subword tokeniser, ByteSpan, that uses an external byte-level LM during training to identify contiguous predictable byte sequences and group them into subwords. Experiments show that ByteSpan yields efficient vocabularies with higher morphological alignment scores than BPE for English. Multilingual experiments show similar compression and R\'enyi efficiency for 25 languages.

Modern language models mostly take sub-words as input, a design that balances the trade-off between vocabulary size, number of parameters, and performance. However, sub-word tokenization still has disadvantages like not being robust to noise and difficult to generalize to new languages. Also, the current trend of scaling up models reveals that larger models require larger embeddings but that makes parallelization hard. Previous work on image classification proves splitting raw input into a sequence of chucks is a strong, model-agnostic inductive bias. Based on this observation, we rethink the existing character-aware method that takes character-level inputs but makes word-level sequence modeling and prediction. We overhaul this method by introducing a cross-attention network that builds word-level representation directly from bytes, and a sub-word level prediction based on word-level hidden states to avoid the time and space requirement of word-level prediction. With these two improvements combined, we have a token free model with slim input embeddings for downstream tasks. We name our method Byte2Word and perform evaluations on language modeling and text classification. Experiments show that Byte2Word is on par with the strong sub-word baseline BERT but only takes up 10\% of embedding size. We further test our method on synthetic noise and cross-lingual transfer and find it competitive to baseline methods on both settings.

We present a novel approach to feature labeling using gradient descent in token-space. While existing methods typically use language models to generate hypotheses about feature meanings, our method directly optimizes label representations by using a language model as a discriminator to predict feature activations. We formulate this as a multi-objective optimization problem in token-space, balancing prediction accuracy, entropy minimization, and linguistic naturalness. Our proof-of-concept experiments demonstrate successful convergence to interpretable single-token labels across diverse domains, including features for detecting animals, mammals, Chinese text, and numbers. Although our current implementation is constrained to single-token labels and relatively simple features, the results suggest that token-space gradient descent could become a valuable addition to the interpretability researcher's toolkit.

We explore the Iterative Inference Hypothesis (IIH) within the context of transformer-based language models, aiming to understand how a model's latent representations are progressively refined and whether observable differences are present between correct and incorrect generations. Our findings provide empirical support for the IIH, showing that the nth token embedding in the residual stream follows a trajectory of decreasing loss. Additionally, we observe that the rate at which residual embeddings converge to a stable output representation reflects uncertainty in the token generation process. Finally, we introduce a method utilizing cross-entropy to detect this uncertainty and demonstrate its potential to distinguish between correct and incorrect token generations on a dataset of idioms.

Entropy-based deep reasoning has emerged as a promising direction for improving the reasoning capabilities of Large Language Models (LLMs), but existing methods often either increase response length indiscriminately or shorten responses at the cost of accuracy. To better balance this trade-off, we introduce Conditional Entropy Shaping (CES), a framework that dynamically controls token-level response entropy, enabling LLMs to produce concise solutions on simple problems while encouraging deeper exploration on hard ones. Built on DAPO, CES uses token-level entropy as an uncertainty signal and applies a conditional bidirectional policy: it penalizes high-entropy "forking point" tokens on correct reasoning paths to improve conciseness, and rewards them on incorrect paths to encourage exploration and error correction. We implement CES on DeepSeek-R1-Distill-7B and evaluate it on 12 mathematical benchmarks. CES consistently improves average accuracy while reducing response length relative to DAPO, and supplementary experiments show similar trends on a smaller 1.5B backbone and on out-of-domain benchmarks.

Large language models such as GPT and Llama are trained with a next-token prediction loss. In this work, we suggest that training language models to predict multiple future tokens at once results in higher sample efficiency. More specifically, at each position in the training corpus, we ask the model to predict the following n tokens using n independent output heads, operating on top of a shared model trunk. Considering multi-token prediction as an auxiliary training task, we measure improved downstream capabilities with no overhead in training time for both code and natural language models. The method is increasingly useful for larger model sizes, and keeps its appeal when training for multiple epochs. Gains are especially pronounced on generative benchmarks like coding, where our models consistently outperform strong baselines by several percentage points. Our 13B parameter models solves 12 % more problems on HumanEval and 17 % more on MBPP than comparable next-token models. Experiments on small algorithmic tasks demonstrate that multi-token prediction is favorable for the development of induction heads and algorithmic reasoning capabilities. As an additional benefit, models trained with 4-token prediction are up to 3 times faster at inference, even with large batch sizes.

In this short report, we introduce joint multi-token prediction (JTP), a lightweight modification of standard next-token prediction designed to enrich hidden state representations by jointly predicting multiple future tokens. Unlike previous multi-token prediction approaches, JTP strategically employs teacher forcing of future-tokens through a carefully designed representation bottleneck, allowing the model to encode rich predictive information with minimal computational overhead during training. We show that the JTP approach achieves a short-horizon belief state representation, while popular alternatives for multi-token prediction fail to do so. We demonstrate the effectiveness of our method on the synthetic star graph navigation task from from Bachmann and Nagarajan [2024], highlighting a significant performance improvement over existing methods. This manuscript presents promising preliminary results intended to stimulate further research.

Recent advances in multimodal large reasoning models (MLRMs) have substantially improved their ability to solve complex textual and visual tasks. However, these models tend to overthink on simple problems, producing unnecessarily lengthy reasoning traces, while under-exploring on challenging ones, leading to missed solutions. To address this imbalance, we propose ARES, a unified open-source framework for adaptive reasoning that dynamically allocates exploration effort based on task difficulty. Our approach is motivated by two key empirical findings: (i) while single-token entropy is noisy, high window-entropy (HWE) tokens (token-level entropies averaged under a sliding window) can reliably capture reasoning-critical moments; and (ii) reducing HWE usage benefits easy problems, while increasing it is essential for solving hard ones. Building on these insights, ARES introduces a two-stage training pipeline. In the Adaptive Cold-Start stage, we curate multimodal and textual data paired with reasoning traces of length proportional to problem difficulty, equipping the model with initial difficulty awareness. In the second stage, we develop Adaptive Entropy Policy Optimization (AEPO), which uses HWE tokens as exploration triggers to decide when to explore, and a hierarchical entropy reward with dynamic KL control to decide how much to explore. Extensive experiments demonstrate that ARES achieves superior performance and reasoning efficiency across diverse mathematical, logical, and multimodal benchmarks, while closing the gap to leading commercial systems under significantly lower inference costs.

Large language models (LLMs) exhibit latent multi-token prediction (MTP) capabilities despite being trained solely for next-token generation. We propose a simple, training-free MTP approach that probes an LLM using on-the-fly mask tokens drawn from its embedding space, enabling parallel prediction of future tokens without modifying model weights or relying on auxiliary draft models. Our method constructs a speculative token tree by sampling top-K candidates from mask-token logits and applies a lightweight pruning strategy to retain high-probability continuations. During decoding, candidate predictions are verified in parallel, resulting in lossless generation while substantially reducing the number of model calls and improving token throughput. Across benchmarks, our probing-based MTP consistently outperforms existing training-free baselines, increasing acceptance length by approximately 12\% on LLaMA3 and 8--12\% on Qwen3, and achieving throughput gains of up to 15--19\%. Finally, we provide theoretical insights and empirical evidence showing that decoder layers naturally align mask-token representations with next-token states, enabling accurate multi-step prediction without retraining or auxiliary models.

Large language models (LLMs) have revolutionized the field of natural language processing, extending their strong capabilities into multi-modal domains. Thus, it is vital to define proper and diversified metrics for the evaluation of LLMs. In this paper, we introduce matrix entropy, a novel metric rooted in information theory and geometry principles to quantify the data compression proficiency in LLMs. It reflects the model's ability to extract relevant information and eliminate unnecessary elements, thereby providing insight into the language model's intrinsic capability. Specifically, we demonstrate its applicability in both single-modal (language) and multi-modal settings. For language models, our findings reveal that the matrix entropy of representations follows a scaling law type reduction when the model scales up, serving as a complement to the traditional loss scaling law. For the multi-modal setting, we also propose an evaluation method based on matrix entropy for assessing alignment quality and we find that modern large multi-modal models exhibit great alignment performance.

Autoregressive language models are constrained by their inherently sequential nature, generating one token at a time. This paradigm limits inference speed and parallelism, especially during later stages of generation when the direction and semantics of text are relatively certain. In this work, we propose a novel framework that leverages the inherent knowledge of vanilla autoregressive language models about future tokens, combining techniques to realize this potential and enable simultaneous prediction of multiple subsequent tokens. Our approach introduces several key innovations: (1) a masked-input formulation where multiple future tokens are jointly predicted from a common prefix; (2) a gated LoRA formulation that preserves the original LLM's functionality, while equipping it for multi-token prediction; (3) a lightweight, learnable sampler module that generates coherent sequences from the predicted future tokens; (4) a set of auxiliary training losses, including a consistency loss, to enhance the coherence and accuracy of jointly generated tokens; and (5) a speculative generation strategy that expands tokens quadratically in the future while maintaining high fidelity. Our method achieves significant speedups through supervised fine-tuning on pretrained models. For example, it generates code and math nearly 5x faster, and improves general chat and knowledge tasks by almost 2.5x. These gains come without any loss in quality.

Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the language generation community for the last few years. In this work, we posit that the abstraction of natural language generation as a discrete stochastic process--which allows for an information-theoretic analysis--can provide new insights into the behavior of probabilistic language generators, e.g., why high-probability texts can be dull or repetitive. Humans use language as a means of communicating information, aiming to do so in a simultaneously efficient and error-minimizing manner; in fact, psycholinguistics research suggests humans choose each word in a string with this subconscious goal in mind. We formally define the set of strings that meet this criterion: those for which each word has an information content close to the expected information content, i.e., the conditional entropy of our model. We then propose a simple and efficient procedure for enforcing this criterion when generating from probabilistic models, which we call locally typical sampling. Automatic and human evaluations show that, in comparison to nucleus and top-k sampling, locally typical sampling offers competitive performance (in both abstractive summarization and story generation) in terms of quality while consistently reducing degenerate repetitions.

We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in natural language is challenging because of "semantic equivalence" -- different sentences can mean the same thing. To overcome these challenges we introduce semantic entropy -- an entropy which incorporates linguistic invariances created by shared meanings. Our method is unsupervised, uses only a single model, and requires no modifications to off-the-shelf language models. In comprehensive ablation studies we show that the semantic entropy is more predictive of model accuracy on question answering data sets than comparable baselines.

Large Reasoning Models (LRMs) often suffer from overthinking, generating unnecessarily long reasoning chains even for simple tasks. This leads to substantial computational overhead with limited performance gain, primarily due to redundant verification and repetitive generation. While prior work typically constrains output length or optimizes correctness, such coarse supervision fails to guide models toward concise yet accurate inference. In this paper, we propose ENTRA, an entropy-based training framework that suppresses redundant reasoning while preserving performance. ENTRA first estimates the token-level importance using a lightweight Bidirectional Importance Estimation (BIE) method, which accounts for both prediction confidence and forward influence. It then computes a redundancy reward based on the entropy of low-importance tokens, normalized by its theoretical upper bound, and optimizes this reward via reinforcement learning. Experiments on mathematical reasoning benchmarks demonstrate that ENTRA reduces output length by 37% to 53% with no loss-and in some cases, gains-in accuracy. Our approach offers a principled and efficient solution to reduce overthinking in LRMs, and provides a generalizable path toward redundancy-aware reasoning optimization.

Fast weight architectures offer a promising alternative to attention-based transformers for long-context modeling by maintaining constant memory overhead regardless of context length. However, their potential is limited by the next-token prediction (NTP) training paradigm. NTP optimizes single-token predictions and ignores semantic coherence across multiple tokens following a prefix. Consequently, fast weight models, which dynamically update their parameters to store contextual information, learn suboptimal representations that fail to capture long-range dependencies. We introduce REFINE (Reinforced Fast weIghts with Next sEquence prediction), a reinforcement learning framework that trains fast weight models under the next-sequence prediction (NSP) objective. REFINE selects informative token positions based on prediction entropy, generates multi-token rollouts, assigns self-supervised sequence-level rewards, and optimizes the model with group relative policy optimization (GRPO). REFINE is applicable throughout the training lifecycle of pre-trained language models: mid-training, post-training, and test-time training. Our experiments on LaCT-760M and DeltaNet-1.3B demonstrate that REFINE consistently outperforms supervised fine-tuning with NTP across needle-in-a-haystack retrieval, long-context question answering, and diverse tasks in LongBench. REFINE provides an effective and versatile framework for improving long-context modeling in fast weight architectures.

Supervised Fine-Tuning (SFT) is the standard paradigm for domain adaptation, yet it frequently incurs the cost of catastrophic forgetting. In sharp contrast, on-policy Reinforcement Learning (RL) effectively preserves general capabilities. We investigate this discrepancy and identify a fundamental distributional gap: while RL aligns with the model's internal belief, SFT forces the model to fit external supervision. This mismatch often manifests as "Confident Conflicts" tokens characterized by low probability but low entropy. In these instances, the model is highly confident in its own prediction but is forced to learn a divergent ground truth, triggering destructive gradient updates. To address this, we propose Entropy-Adaptive Fine-Tuning (EAFT). Unlike methods relying solely on prediction probability, EAFT utilizes token-level entropy as a gating mechanism to distinguish between epistemic uncertainty and knowledge conflict. This allows the model to learn from uncertain samples while suppressing gradients on conflicting data. Extensive experiments on Qwen and GLM series (ranging from 4B to 32B parameters) across mathematical, medical, and agentic domains confirm our hypothesis. EAFT consistently matches the downstream performance of standard SFT while significantly mitigating the degradation of general capabilities.

Language models are pretrained as passive predictors with no incentive to model the consequences of their own outputs. Post-training changes this: a model producing its own responses can benefit from recognizing that it is on-policy. We present evidence that post-trained models recognize their on-policy generations, and this recognition is implicitly encoded in their output distributions. In particular, on-policy output distribution entropy is 3--4times lower than off-policy entropy, across model families and size classes. We trace part of this effect to an internal representation of input surprise, tracking the unlikeliness of the most recent input token according to the model's prior predictions, that causally modulates output entropy. One example of these phenomena can be observed in response to open-ended prompts; post-trained models (unlike pretrained models) collapse their uncertainty over the topic of their upcoming response before the first output token; violating this cached intention with a different-topic prefill results in higher output entropy. We also tested whether models can distinguish on-policy contexts from prefills via explicit verbal report. We find that they can, but that interestingly, this explicit recognition routes through a different mechanism than implicit recognition.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

Large language models (LLMs) have been widely employed across various application domains, yet their black-box nature poses significant challenges to understanding how these models process input data internally to make predictions. In this paper, we introduce a precise and quantitative law that governs the learning of contextualized token embeddings through intermediate layers in pre-trained LLMs for next-token prediction. Our findings reveal that each layer contributes equally to enhancing prediction accuracy, from the lowest to the highest layer -- a universal phenomenon observed across a diverse array of open-source LLMs, built on architectures such as Transformer, RWKV, and Mamba. We demonstrate that this law offers new perspectives and insights to inform and guide practices in LLM development and applications, including model scaling, pre-training tasks, and information flow. Overall, our law enables more fine-grained approaches to the design, training, and interpretation of LLMs through scrutinizing their internal data processing mechanisms.

We explore the properties of byte-level recurrent language models. When given sufficient amounts of capacity, training data, and compute time, the representations learned by these models include disentangled features corresponding to high-level concepts. Specifically, we find a single unit which performs sentiment analysis. These representations, learned in an unsupervised manner, achieve state of the art on the binary subset of the Stanford Sentiment Treebank. They are also very data efficient. When using only a handful of labeled examples, our approach matches the performance of strong baselines trained on full datasets. We also demonstrate the sentiment unit has a direct influence on the generative process of the model. Simply fixing its value to be positive or negative generates samples with the corresponding positive or negative sentiment.

Language models typically tokenize text into subwords, using a deterministic, hand-engineered heuristic of combining characters into longer surface-level strings such as 'ing' or whole words. Recent literature has repeatedly shown the limitations of such a tokenization strategy, particularly for documents not written in English and for representing numbers. On the other extreme, byte/character-level language models are much less restricted but suffer from increased sequence description lengths and a subsequent quadratic expansion in self-attention computation. Recent attempts to compress and limit these context lengths with fixed size convolutions is helpful but completely ignores the word boundary. This paper considers an alternative 'learn your tokens' scheme which utilizes the word boundary to pool bytes/characters into word representations, which are fed to the primary language model, before again decoding individual characters/bytes per word in parallel. We find that our moderately expressive and moderately fast end-to-end tokenizer outperform by over 300% both subwords and byte/character models over the intrinsic language modeling metric of next-word prediction across datasets. It particularly outshines on rare words, outperforming by a factor of 30! We extensively study the language modeling setup for all three categories of tokenizers and theoretically analyze how our end-to-end models can also be a strong trade-off in efficiency and robustness.

Large Language Models (LLMs) rely on the Key-Value (KV) Cache to store token history, enabling efficient decoding of tokens. As the KV-Cache grows, it becomes a major memory and computation bottleneck, however, there is an opportunity to alleviate this bottleneck, especially because prior research has shown that only a small subset of tokens contribute meaningfully to each decoding step. A key challenge in finding these critical tokens is that they are dynamic, and heavily input query-dependent. Existing methods either risk quality by evicting tokens permanently, or retain the full KV-Cache but rely on retrieving chunks (pages) of tokens at generation, failing at dense, context-rich tasks. Additionally, many existing KV-Cache sparsity methods rely on inaccurate proxies for token importance. To address these limitations, we introduce TokenButler, a high-granularity, query-aware predictor that learns to identify these critical tokens. By training a light-weight predictor with less than 1.2% parameter overhead, TokenButler prioritizes tokens based on their contextual, predicted importance. This improves perplexity & downstream accuracy by over 8% relative to SoTA methods for estimating token importance. We evaluate TokenButler on a novel synthetic small-context co-referential retrieval task, demonstrating near-oracle accuracy. Code, models and benchmarks: https://github.com/abdelfattah-lab/TokenButler

Estimating the difficulty of input questions as perceived by large language models (LLMs) is essential for accurate performance evaluation and adaptive inference. Existing methods typically rely on repeated response sampling, auxiliary models, or fine-tuning the target model itself, which may incur substantial computational costs or compromise generality. In this paper, we propose a novel approach for difficulty estimation that leverages only the hidden representations produced by the target LLM. We model the token-level generation process as a Markov chain and define a value function to estimate the expected output quality given any hidden state. This allows for efficient and accurate difficulty estimation based solely on the initial hidden state, without generating any output tokens. Extensive experiments across both textual and multimodal tasks demonstrate that our method consistently outperforms existing baselines in difficulty estimation. Moreover, we apply our difficulty estimates to guide adaptive reasoning strategies, including Self-Consistency, Best-of-N, and Self-Refine, achieving higher inference efficiency with fewer generated tokens.

Embedding layers in transformer-based NLP models typically account for the largest share of model parameters, scaling with vocabulary size but not yielding performance gains proportional to scale. We propose an alternative approach in which token embedding vectors are first generated deterministically, directly from the token IDs using a Fourier expansion of their normalized values, followed by a lightweight multilayer perceptron (MLP) that captures higher-order interactions. We train standard transformers and our architecture on natural language inference tasks (SNLI and MNLI), and evaluate zero-shot performance on sentence textual similarity (STS-B). Our results demonstrate that the proposed method achieves competitive performance using significantly fewer parameters, trains faster, and operates effectively without the need for dropout. This proof-of-concept study highlights the potential for scalable, memory-efficient language models and motivates further large-scale experimentation based on our findings.

Language models have recently been shown capable of performing regression tasks wherein numeric predictions are represented as decoded strings. In this work, we provide theoretical grounds for this capability and furthermore investigate the utility of causal auto-regressive sequence models when they are applied to any feature representation. We find that, despite being trained in the usual way - for next-token prediction via cross-entropy loss - decoding-based regression is as performant as traditional approaches for tabular regression tasks, while being flexible enough to capture arbitrary distributions, such as in the task of density estimation.

This paper introduces the counter-intuitive generalization results of overfitting pre-trained large language models (LLMs) on very small datasets. In the setting of open-ended text generation, it is well-documented that LLMs tend to generate repetitive and dull sequences, a phenomenon that is especially apparent when generating using greedy decoding. This issue persists even with state-of-the-art LLMs containing billions of parameters, trained via next-token prediction on large datasets. We find that by further fine-tuning these models to achieve a near-zero training loss on a small set of samples -- a process we refer to as hyperfitting -- the long-sequence generative capabilities are greatly enhanced. Greedy decoding with these Hyperfitted models even outperform Top-P sampling over long-sequences, both in terms of diversity and human preferences. This phenomenon extends to LLMs of various sizes, different domains, and even autoregressive image generation. We further find this phenomena to be distinctly different from that of Grokking and double descent. Surprisingly, our experiments indicate that hyperfitted models rarely fall into repeating sequences they were trained on, and even explicitly blocking these sequences results in high-quality output. All hyperfitted models produce extremely low-entropy predictions, often allocating nearly all probability to a single token.

Autoregressive language models generate text one token at a time, yet natural language is inherently structured in multi-token units, including phrases, n-grams, and collocations that carry meaning jointly. This one-token bottleneck limits both the expressiveness of the model during pre-training and its throughput at inference time. Existing remedies such as speculative decoding or diffusion-based language models either leave the underlying bottleneck intact or sacrifice the causal structure essential to language modeling. We propose BitLM, a language model that represents each token as a fixed-length binary code and employs a lightweight diffusion head to denoise multiple tokens in parallel within each block. Crucially, BitLM preserves left-to-right causal attention across blocks while making joint lexical decisions within each block, combining the reliability of autoregressive modeling with the parallelism of iterative refinement. By replacing the large-vocabulary softmax with bitwise denoising, BitLM reframes token generation as iterative commitment in a compact binary space, enabling more efficient pre-training and substantially faster inference without altering the causal foundation that makes language models effective. Our results demonstrate that the one-token-at-a-time paradigm is not a fundamental requirement but an interface choice, and that changing it can yield a stronger and faster language model. We hope BitLM points toward a promising direction for next-generation language model architectures.

Masked Language Modeling (MLM) has been one of the most prominent approaches for pretraining bidirectional text encoders due to its simplicity and effectiveness. One notable concern about MLM is that the special [MASK] symbol causes a discrepancy between pretraining data and downstream data as it is present only in pretraining but not in fine-tuning. In this work, we offer a new perspective on the consequence of such a discrepancy: We demonstrate empirically and theoretically that MLM pretraining allocates some model dimensions exclusively for representing [MASK] tokens, resulting in a representation deficiency for real tokens and limiting the pretrained model's expressiveness when it is adapted to downstream data without [MASK] tokens. Motivated by the identified issue, we propose MAE-LM, which pretrains the Masked Autoencoder architecture with MLM where [MASK] tokens are excluded from the encoder. Empirically, we show that MAE-LM improves the utilization of model dimensions for real token representations, and MAE-LM consistently outperforms MLM-pretrained models across different pretraining settings and model sizes when fine-tuned on the GLUE and SQuAD benchmarks.

Auto-regressive language models factorize sequence probabilities and are trained by minimizing the negative log-likelihood (NLL) objective. While empirically powerful, a deep theoretical understanding of why this simple objective yields such versatile representations remains elusive. This work introduces a unifying analytical framework using Markov Categories (MCs) to deconstruct the AR generation process and the NLL objective. We model the single-step generation map as a composition of Markov kernels in the category Stoch. This compositional view, when enriched with statistical divergences, allows us to dissect information flow and learned geometry. Our framework makes three main contributions. First, we provide a formal, information-theoretic rationale for the success of modern speculative decoding methods like EAGLE, quantifying the information surplus in hidden states that these methods exploit. Second, we formalize how NLL minimization forces the model to learn not just the next token, but the data's intrinsic conditional stochasticity, a process we analyze using categorical entropy. Third, and most centrally, we prove that NLL training acts as an implicit form of spectral contrastive learning. By analyzing the information geometry of the model's prediction head, we show that NLL implicitly forces the learned representation space to align with the eigenspectrum of a predictive similarity operator, thereby learning a geometrically structured space without explicit contrastive pairs. This compositional and information-geometric perspective reveals the deep structural principles underlying the effectiveness of modern LMs. Project Page: https://github.com/asiresearch/lm-theory

Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of relevant features to the functional entropy of the network with respect to the input. We rely on the log-Sobolev inequality that bounds the functional entropy by the functional Fisher information with respect to the covariance of the data. This provides a principled way to measure the amount of information contribution of a subset of features to the decision function. Through extensive experiments, we show that our method surpasses existing interpretability sampling-based methods on various data signals such as image, text, and audio.

By encoding time series as a string of numerical digits, we can frame time series forecasting as next-token prediction in text. Developing this approach, we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can surprisingly zero-shot extrapolate time series at a level comparable to or exceeding the performance of purpose-built time series models trained on the downstream tasks. To facilitate this performance, we propose procedures for effectively tokenizing time series data and converting discrete distributions over tokens into highly flexible densities over continuous values. We argue the success of LLMs for time series stems from their ability to naturally represent multimodal distributions, in conjunction with biases for simplicity, and repetition, which align with the salient features in many time series, such as repeated seasonal trends. We also show how LLMs can naturally handle missing data without imputation through non-numerical text, accommodate textual side information, and answer questions to help explain predictions. While we find that increasing model size generally improves performance on time series, we show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers, and poor uncertainty calibration, which is likely the result of alignment interventions such as RLHF.

According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple encodings to find the most predictive one. Inspired by Kolmogorov Complexity principles, we propose a single-pass adaptive tokenizer, KARL, which predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL's training procedure closely resembles the Upside-Down Reinforcement Learning paradigm, as it learns to conditionally predict token halting based on a desired reconstruction quality. KARL matches the performance of recent adaptive tokenizers while operating in a single pass. We present scaling laws for KARL, analyzing the role of encoder/decoder size, continuous vs. discrete tokenization and more. Additionally, we offer a conceptual study drawing an analogy between Adaptive Image Tokenization and Algorithmic Information Theory, examining the predicted image complexity (KC) across axes such as structure vs. noise and in- vs. out-of-distribution familiarity -- revealing alignment with human intuition.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful approach to enhancing the reasoning capabilities of Large Language Models (LLMs), while its mechanisms are not yet well understood. In this work, we undertake a pioneering exploration of RLVR through the novel perspective of token entropy patterns, comprehensively analyzing how different tokens influence reasoning performance. By examining token entropy patterns in Chain-of-Thought (CoT) reasoning, we observe that only a small fraction of tokens exhibit high entropy, and these tokens act as critical forks that steer the model toward diverse reasoning pathways. Furthermore, studying how entropy patterns evolve during RLVR training reveals that RLVR largely adheres to the base model's entropy patterns, primarily adjusting the entropy of high-entropy tokens. These findings highlight the significance of high-entropy tokens (i.e., forking tokens) to RLVR. We ultimately improve RLVR by restricting policy gradient updates to forking tokens and uncover a finding even beyond the 80/20 rule: utilizing only 20% of the tokens while maintaining performance comparable to full-gradient updates on the Qwen3-8B base model and significantly surpassing full-gradient updates on the Qwen3-32B (+11.04 on AIME'25 and +7.71 on AIME'24) and Qwen3-14B (+4.79 on AIME'25 and +5.21 on AIME'24) base models, highlighting a strong scaling trend. In contrast, training exclusively on the 80% lowest-entropy tokens leads to a marked decline in performance. These findings indicate that the efficacy of RLVR primarily arises from optimizing the high-entropy tokens that decide reasoning directions. Collectively, our results highlight the potential to understand RLVR through a token-entropy perspective and optimize RLVR by leveraging high-entropy minority tokens to further improve LLM reasoning.

Transformers achieve unrivalled performance in modelling language, but remain inefficient in terms of memory and time complexity. A possible remedy is to reduce the sequence length in the intermediate layers by pooling fixed-length segments of tokens. Nevertheless, natural units of meaning, such as words or phrases, display varying sizes. To address this mismatch, we equip language models with a dynamic-pooling mechanism, which predicts segment boundaries in an autoregressive fashion. We compare several methods to infer boundaries, including end-to-end learning through stochastic re-parameterisation, supervised learning (based on segmentations from subword tokenizers or spikes in conditional entropy), as well as linguistically motivated boundaries. We perform character-level evaluation on texts from multiple datasets and morphologically diverse languages. The results demonstrate that dynamic pooling, which jointly segments and models language, is both faster and more accurate than vanilla Transformers and fixed-length pooling within the same computational budget.

Time series forecasting plays a vital role in supporting decision-making across a wide range of critical applications, including energy, healthcare, and finance. Despite recent advances, forecasting accuracy remains limited due to the challenge of integrating historical numerical sequences with contextual features, which often comprise unstructured textual data. To address this challenge, we propose TokenCast, an LLM-driven framework that leverages language-based symbolic representations as a unified intermediary for context-aware time series forecasting. Specifically, TokenCast employs a discrete tokenizer to transform continuous numerical sequences into temporal tokens, enabling structural alignment with language-based inputs. To bridge the semantic gap between modalities, both temporal and contextual tokens are embedded into a shared representation space via a pre-trained large language model (LLM), further optimized with autoregressive generative objectives. Building upon this unified semantic space, the aligned LLM is subsequently fine-tuned in a supervised manner to predict future temporal tokens, which are then decoded back into the original numerical space. Extensive experiments on diverse real-world datasets enriched with contextual features demonstrate the effectiveness and generalizability of TokenCast.

We propose Next Concept Prediction (NCP), a generative pretraining paradigm built on top of Next Token Prediction (NTP). NCP predicts discrete concepts that span multiple tokens, thereby forming a more challenging pretraining objective. Our model, ConceptLM, quantizes hidden states using Vector Quantization and constructs a concept vocabulary. It leverages both NCP and NTP to drive parameter updates and generates a concept to guide the generation of the following tokens. We train ConceptLM from scratch at scales ranging from 70M to 1.5B parameters with up to 300B training data, including Pythia and GPT-2 backbones. Results on 13 benchmarks show that NCP yields consistent performance gains over traditional token-level models. Furthermore, continual pretraining experiments on an 8B-parameter Llama model indicate that NCP can further improve an NTP-trained model. Our analysis suggests that NCP leads to more powerful language models by introducing a harder pretraining task, providing a promising path toward better language modeling.

As the scale of training corpora for large language models (LLMs) grows, model developers become increasingly reluctant to disclose details on their data. This lack of transparency poses challenges to scientific evaluation and ethical deployment. Recently, pretraining data detection approaches, which infer whether a given text was part of an LLM's training data through black-box access, have been explored. The Min-K\% Prob method, which has achieved state-of-the-art results, assumes that a non-training example tends to contain a few outlier words with low token probabilities. However, the effectiveness may be limited as it tends to misclassify non-training texts that contain many common words with high probabilities predicted by LLMs. To address this issue, we introduce a divergence-based calibration method, inspired by the divergence-from-randomness concept, to calibrate token probabilities for pretraining data detection. We compute the cross-entropy (i.e., the divergence) between the token probability distribution and the token frequency distribution to derive a detection score. We have developed a Chinese-language benchmark, PatentMIA, to assess the performance of detection approaches for LLMs on Chinese text. Experimental results on English-language benchmarks and PatentMIA demonstrate that our proposed method significantly outperforms existing methods. Our code and PatentMIA benchmark are available at https://github.com/zhang-wei-chao/DC-PDD.

When using agent-task datasets to enhance agent capabilities for Large Language Models (LLMs), current methodologies often treat all tokens within a sample equally. However, we argue that tokens serving different roles - specifically, reasoning tokens versus boilerplate tokens (e.g., those governing output format) - differ significantly in importance and learning complexity, necessitating their disentanglement and distinct treatment. To address this, we propose a novel Shuffle-Aware Discriminator (SHAD) for adaptive token discrimination. SHAD classifies tokens by exploiting predictability differences observed after shuffling input-output combinations across samples: boilerplate tokens, due to their repetitive nature among samples, maintain predictability, whereas reasoning tokens do not. Using SHAD, we propose the Reasoning-highlighted Fine-Tuning (RFT) method, which adaptively emphasizes reasoning tokens during fine-tuning, yielding notable performance gains over common Supervised Fine-Tuning (SFT).

We propose semantic entropy probes (SEPs), a cheap and reliable method for uncertainty quantification in Large Language Models (LLMs). Hallucinations, which are plausible-sounding but factually incorrect and arbitrary model generations, present a major challenge to the practical adoption of LLMs. Recent work by Farquhar et al. (2024) proposes semantic entropy (SE), which can detect hallucinations by estimating uncertainty in the space semantic meaning for a set of model generations. However, the 5-to-10-fold increase in computation cost associated with SE computation hinders practical adoption. To address this, we propose SEPs, which directly approximate SE from the hidden states of a single generation. SEPs are simple to train and do not require sampling multiple model generations at test time, reducing the overhead of semantic uncertainty quantification to almost zero. We show that SEPs retain high performance for hallucination detection and generalize better to out-of-distribution data than previous probing methods that directly predict model accuracy. Our results across models and tasks suggest that model hidden states capture SE, and our ablation studies give further insights into the token positions and model layers for which this is the case.

Large Language Models (LLMs) have revolutionized natural language processing but can exhibit biases and may generate toxic content. While alignment techniques like Reinforcement Learning from Human Feedback (RLHF) reduce these issues, their impact on creativity, defined as syntactic and semantic diversity, remains unexplored. We investigate the unintended consequences of RLHF on the creativity of LLMs through three experiments focusing on the Llama-2 series. Our findings reveal that aligned models exhibit lower entropy in token predictions, form distinct clusters in the embedding space, and gravitate towards "attractor states", indicating limited output diversity. Our findings have significant implications for marketers who rely on LLMs for creative tasks such as copywriting, ad creation, and customer persona generation. The trade-off between consistency and creativity in aligned models should be carefully considered when selecting the appropriate model for a given application. We also discuss the importance of prompt engineering in harnessing the creative potential of base models.

Large Language Models achieve next-token prediction by transporting a vectorized piece of text (prompt) across an accompanying embedding space under the action of successive transformer layers. The resulting high-dimensional trajectories realize different contextualization, or 'thinking', steps, and fully determine the output probability distribution. We aim to characterize the statistical properties of ensembles of these 'lines of thought.' We observe that independent trajectories cluster along a low-dimensional, non-Euclidean manifold, and that their path can be well approximated by a stochastic equation with few parameters extracted from data. We find it remarkable that the vast complexity of such large models can be reduced to a much simpler form, and we reflect on implications.

Vision Large Language Models (VLLMs) incur high computational costs due to their reliance on hundreds of visual tokens to represent images. While token pruning offers a promising solution for accelerating inference, this paper, however, identifies a key observation: in deeper layers (e.g., beyond the 20th), existing training-free pruning methods perform no better than random pruning. We hypothesize that this degradation is caused by "vanishing token information", where visual tokens progressively lose their salience with increasing network depth. To validate this hypothesis, we quantify a token's information content by measuring the change in the model output probabilities upon its removal. Using this proposed metric, our analysis of the information of visual tokens across layers reveals three key findings: (1) As layers deepen, the information of visual tokens gradually becomes uniform and eventually vanishes at an intermediate layer, which we term as "information horizon", beyond which the visual tokens become redundant; (2) The position of this horizon is not static; it extends deeper for visually intensive tasks, such as Optical Character Recognition (OCR), compared to more general tasks like Visual Question Answering (VQA); (3) This horizon is also strongly correlated with model capacity, as stronger VLLMs (e.g., Qwen2.5-VL) employ deeper visual tokens than weaker models (e.g., LLaVA-1.5). Based on our findings, we show that simple random pruning in deep layers efficiently balances performance and efficiency. Moreover, integrating random pruning consistently enhances existing methods. Using DivPrune with random pruning achieves state-of-the-art results, maintaining 96.9% of Qwen-2.5-VL-7B performance while pruning 50% of visual tokens. The code will be publicly available at https://github.com/YahongWang1/Information-Horizon.

Large language models have shown remarkable performance across a wide range of language tasks, owing to their exceptional capabilities in context modeling. The most commonly used method of context modeling is full self-attention, as seen in standard decoder-only Transformers. Although powerful, this method can be inefficient for long sequences and may overlook inherent input structures. To address these problems, an alternative approach is parallel context encoding, which splits the context into sub-pieces and encodes them parallelly. Because parallel patterns are not encountered during training, naively applying parallel encoding leads to performance degradation. However, the underlying reasons and potential mitigations are unclear. In this work, we provide a detailed analysis of this issue and identify that unusually high attention entropy can be a key factor. Furthermore, we adopt two straightforward methods to reduce attention entropy by incorporating attention sinks and selective mechanisms. Experiments on various tasks reveal that these methods effectively lower irregular attention entropy and narrow performance gaps. We hope this study can illuminate ways to enhance context modeling mechanisms.

Decoding methods for large language models (LLMs) usually struggle with the tradeoff between ensuring factuality and maintaining diversity. For example, a higher p threshold in the nucleus (top-p) sampling increases the diversity but decreases the factuality, and vice versa. In this paper, we propose REAL (Residual Entropy from Asymptotic Line) sampling, a decoding method that achieves improved factuality and diversity over nucleus sampling by predicting an adaptive threshold of p. Specifically, REAL sampling predicts the step-wise likelihood of an LLM to hallucinate, and lowers the p threshold when an LLM is likely to hallucinate. Otherwise, REAL sampling increases the p threshold to boost the diversity. To predict the step-wise hallucination likelihood without supervision, we construct a Token-level Hallucination Forecasting (THF) model to predict the asymptotic entropy (i.e., inherent uncertainty) of the next token by extrapolating the next-token entropies from a series of LLMs with different sizes. If a LLM's entropy is higher than the asymptotic entropy (i.e., the LLM is more uncertain than it should be), the THF model predicts a high hallucination hazard, which leads to a lower p threshold in REAL sampling. In the FactualityPrompts benchmark, we demonstrate that REAL sampling based on a 70M THF model can substantially improve the factuality and diversity of 7B LLMs simultaneously, judged by both retrieval-based metrics and human evaluation. After combined with contrastive decoding, REAL sampling outperforms 9 sampling methods, and generates texts that are more factual than the greedy sampling and more diverse than the nucleus sampling with p=0.5. Furthermore, the predicted asymptotic entropy is also a useful unsupervised signal for hallucination detection tasks.

The rapid growth in the parameters of large language models (LLMs) has made inference latency a fundamental bottleneck, limiting broader application of LLMs. Speculative decoding represents a lossless approach to accelerate inference through a guess-and-verify paradigm, leveraging the parallel capabilities of modern hardware. Some speculative decoding methods rely on additional structures to guess draft tokens, such as small models or parameter-efficient architectures, which need extra training before use. Alternatively, retrieval-based train-free techniques build libraries from pre-existing corpora or by n-gram generation. However, they face challenges like large storage requirements, time-consuming retrieval, and limited adaptability. Observing that candidate tokens generated during the decoding process are likely to reoccur in future sequences, we propose Token Recycling. This approach stores candidate tokens in an adjacency matrix and employs a breadth-first search (BFS)-like algorithm on the matrix to construct a draft tree. The tree is then validated through tree attention. New candidate tokens from the decoding process are then used to update the matrix. Token Recycling requires \textless2MB of additional storage and achieves approximately 2x speedup across all sizes of LLMs. It significantly outperforms existing train-free methods by 30\% and even a training method by 25\%. It can be directly applied to any existing LLMs and tasks without the need for adaptation.

Decoder-only autoregressive image generation typically relies on fixed-length tokenization schemes whose token counts grow quadratically with resolution, substantially increasing the computational and memory demands of attention. We present DPAR, a novel decoder-only autoregressive model that dynamically aggregates image tokens into a variable number of patches for efficient image generation. Our work is the first to demonstrate that next-token prediction entropy from a lightweight and unsupervised autoregressive model provides a reliable criterion for merging tokens into larger patches based on information content. DPAR makes minimal modifications to the standard decoder architecture, ensuring compatibility with multimodal generation frameworks and allocating more compute to generation of high-information image regions. Further, we demonstrate that training with dynamically sized patches yields representations that are robust to patch boundaries, allowing DPAR to scale to larger patch sizes at inference. DPAR reduces token count by 1.81x and 2.06x on Imagenet 256 and 384 generation resolution respectively, leading to a reduction of up to 40% FLOPs in training costs. Further, our method exhibits faster convergence and improves FID by up to 27.1% relative to baseline models.

While speculative decoding has recently appeared as a promising direction for accelerating the inference of large language models (LLMs), the speedup and scalability are strongly bounded by the token acceptance rate. Prevalent methods usually organize predicted tokens as independent chains or fixed token trees, which fails to generalize to diverse query distributions. In this paper, we propose DySpec, a faster speculative decoding algorithm with a novel dynamic token tree structure. We begin by bridging the draft distribution and acceptance rate from intuitive and empirical clues, and successfully show that the two variables are strongly correlated. Based on this, we employ a greedy strategy to dynamically expand the token tree at run time. Theoretically, we show that our method can achieve optimal results under mild assumptions. Empirically, DySpec yields a higher acceptance rate and speedup than fixed trees. DySpec can drastically improve the throughput and reduce the latency of token generation across various data distribution and model sizes, which significantly outperforms strong competitors, including Specinfer and Sequoia. Under low temperature setting, DySpec can improve the throughput up to 9.1times and reduce the latency up to 9.4times on Llama2-70B. Under high temperature setting, DySpec can also improve the throughput up to 6.21times, despite the increasing difficulty of speculating more than one token per step for draft model.

A significant use case of instruction-finetuned Large Language Models (LLMs) is to solve question-answering tasks interactively. In this setting, an LLM agent is tasked with making a prediction by sequentially querying relevant information from the user, as opposed to a single-turn conversation. This paper explores sequential querying strategies that aim to minimize the expected number of queries. One such strategy is Information Pursuit (IP), a greedy algorithm that at each iteration selects the query that maximizes information gain or equivalently minimizes uncertainty. However, obtaining accurate estimates of mutual information or conditional entropy for LLMs is very difficult in practice due to over- or under-confident LLM probabilities, which leads to suboptimal query selection and predictive performance. To better estimate the uncertainty at each iteration, we propose Conformal Information Pursuit (C-IP), an alternative approach to sequential information gain based on conformal prediction sets. More specifically, C-IP leverages a relationship between prediction sets and conditional entropy at each iteration to estimate uncertainty based on the average size of conformal prediction sets. In contrast to conditional entropy, we find that conformal prediction sets are a distribution-free and robust method of measuring uncertainty. Experiments with 20 Questions show that C-IP obtains better predictive performance and shorter query-answer chains compared to previous approaches to IP and uncertainty-based chain-of-thought methods. Furthermore, extending to an interactive medical setting between a doctor and a patient on the MediQ dataset, C-IP achieves competitive performance with direct single-turn prediction while offering greater interpretability.

Generative models, from diffusion models to large language models, achieve remarkable performance but at a cost in training data orders of magnitude larger than what biological learners require. An alternative paradigm has emerged in which networks are trained to predict their own latent representations of related views or masked regions, as in data2vec and JEPA -- an idea related to predictive-coding accounts of the cortex. Despite strong empirical results, the theoretical understanding of these methods remains limited. Central questions include: by how much does latent prediction actually improve data efficiency? Is there a benefit to stacking such methods into multi-scale hierarchies? We answer both using as data a tractable probabilistic context-free grammar that captures the compositional structure of natural language and images. Such a grammar generates strings of visible tokens by recursively applying production rules along a tree of hidden symbols of depth L. For such data, supervised or token-level SSL require a number of samples exponential in L to recover the latent tree; we prove that latent prediction achieves this with a number of samples constant in L, up to logarithmic factors. We confirm this bound with (i) a hierarchical clustering algorithm, (ii) an end-to-end neural network whose predictor-clusterer modules predict their own latents at each level via gradient descent, and (iii) the first sample-complexity analysis of data2vec, which we show implicitly performs hierarchical latent prediction. This suggests that explicit stacking such as H-JEPA is largely redundant.

Reinforcement learning (RL) is a pivotal task for enhancing Large Language Model (LLM) reasoning. Conventional algorithms, however, typically adhere to a coarse-grained credit assignment paradigm, applying a uniform reward to all tokens in a sequence, a critical flaw in long-chain reasoning tasks. In this paper, we address this challenge and propose Dynamic Entropy Weighting, a novel mechanism that facilitates fine-grained rewards through two new algorithms: Group Token Policy Optimization (GTPO), which assigns an entropy-weighted reward to each token, and the analogous algorithm Sequence-Level GRPO (GRPO-S). Our approach is founded on the hypothesis that high policy entropy within a reasoning path is a powerful heuristic for cognitive effort at pivotal junctures, which can be repurposed into a learning signal. By repurposing policy entropy for reward shaping, we achieve true per-token credit assignment. Experimental results across challenging reasoning benchmarks validate the superiority of our approach, showing our methods significantly outperform a strong DAPO baseline and confirming our entropy-weighting mechanism as the key driver of this performance boost.

Subword tokenization is an essential part of modern large language models (LLMs), yet its specific contributions to training efficiency and model performance remain poorly understood. In this work, we decouple the effects of subword tokenization by isolating them within a controlled byte-level pretraining pipeline. We formulate and test hypotheses across various dimensions, including sample throughput, vocabulary scaling, and the linguistic prior of subword boundaries. By simulating these effects in a byte-level setting, we refine our understanding of why subword models outperform raw byte models and offer insights to improve the pretraining of future byte-level and subword models. Specifically, our experiments highlight the critical role of increased training throughput and the integration of subword boundaries as either explicit priors or inductive biases.

Large language models (LLMs) demonstrate great performance in text generation. However, LLMs are still suffering from hallucinations. In this work, we propose an inference-time method, Self-Highlighted Hesitation (SH2), to help LLMs decode more truthfully. SH2 is based on a simple fact rooted in information theory that for an LLM, the tokens predicted with lower probabilities are prone to be more informative than others. Our analysis shows that the tokens assigned with lower probabilities by an LLM are more likely to be closely related to factual information, such as nouns, proper nouns, and adjectives. Therefore, we propose to ''highlight'' the factual information by selecting the tokens with the lowest probabilities and concatenating them to the original context, thus forcing the model to repeatedly read and hesitate on these tokens before generation. During decoding, we also adopt contrastive decoding to emphasize the difference in the output probabilities brought by the hesitation. Experimental results demonstrate that our SH2, requiring no additional data or models, can effectively help LLMs elicit factual knowledge and distinguish hallucinated contexts. Significant and consistent improvements are achieved by SH2 for LLaMA-7b and LLaMA2-7b on multiple hallucination tasks.

We conjecture that hidden state vectors corresponding to individual input tokens encode information sufficient to accurately predict several tokens ahead. More concretely, in this paper we ask: Given a hidden (internal) representation of a single token at position t in an input, can we reliably anticipate the tokens that will appear at positions geq t + 2? To test this, we measure linear approximation and causal intervention methods in GPT-J-6B to evaluate the degree to which individual hidden states in the network contain signal rich enough to predict future hidden states and, ultimately, token outputs. We find that, at some layers, we can approximate a model's output with more than 48% accuracy with respect to its prediction of subsequent tokens through a single hidden state. Finally we present a "Future Lens" visualization that uses these methods to create a new view of transformer states.

A popular approach to post-training control of large language models (LLMs) is the steering of intermediate latent representations. Namely, identify a well-chosen direction depending on the task at hand and perturbs representations along this direction at inference time. While many propositions exist to pick this direction, considerably less is understood about how to choose the magnitude of the move, whereas its importance is clear: too little and the intended behavior does not emerge, too much and the model's performance degrades beyond repair. In this work, we propose the first theoretical analysis of steering strength. We characterize its effect on next token probability, presence of a concept, and cross-entropy, deriving precise qualitative laws governing these quantities. Our analysis reveals surprising behaviors, including non-monotonic effects of steering strength. We validate our theoretical predictions empirically on eleven language models, ranging from a small GPT architecture to modern models.

Entropy serves as a critical metric for measuring the diversity of outputs generated by large language models (LLMs), providing valuable insights into their exploration capabilities. While recent studies increasingly focus on monitoring and adjusting entropy to better balance exploration and exploitation in reinforcement fine-tuning (RFT), a principled understanding of entropy dynamics during this process is yet to be thoroughly investigated. In this paper, we establish a theoretical framework for analyzing the entropy dynamics during the RFT process, which begins with a discriminant expression that quantifies entropy change under a single logit update. This foundation enables the derivation of a first-order expression for entropy change, which can be further extended to the update formula of Group Relative Policy Optimization (GRPO). The corollaries and insights drawn from the theoretical analysis inspire the design of entropy control methods, and also offer a unified lens for interpreting various entropy-based methods in existing studies. We provide empirical evidence to support the main conclusions of our analysis and demonstrate the effectiveness of the derived entropy-discriminator clipping methods. This study yields novel insights into RFT training dynamics, providing theoretical support and practical strategies for optimizing the exploration-exploitation balance during LLM fine-tuning.

It has long been established that predictive models can be transformed into lossless compressors and vice versa. Incidentally, in recent years, the machine learning community has focused on training increasingly large and powerful self-supervised (language) models. Since these large language models exhibit impressive predictive capabilities, they are well-positioned to be strong compressors. In this work, we advocate for viewing the prediction problem through the lens of compression and evaluate the compression capabilities of large (foundation) models. We show that large language models are powerful general-purpose predictors and that the compression viewpoint provides novel insights into scaling laws, tokenization, and in-context learning. For example, Chinchilla 70B, while trained primarily on text, compresses ImageNet patches to 43.4% and LibriSpeech samples to 16.4% of their raw size, beating domain-specific compressors like PNG (58.5%) or FLAC (30.3%), respectively. Finally, we show that the prediction-compression equivalence allows us to use any compressor (like gzip) to build a conditional generative model.

Adapting decoder-only multimodal large language models (MLLMs) for unified multimodal retrieval faces two structural gaps. First, existing methods rely on implicit pooling, which overloads the hidden state of a standard vocabulary token (e.g., <EOS>) as the sequence-level representation, a mechanism never designed for information aggregation. Second, contrastive fine-tuning specifies what the embedding should match but provides no token-level guidance on how information should be compressed into it. We address both gaps with two complementary components. Architecturally, we introduce Bottleneck Tokens (BToks), a small set of learnable tokens that serve as a fixed-capacity explicit pooling mechanism. For training, we propose Generative Information Condensation: a next-token prediction objective coupled with a Condensation Mask that severs the direct attention path from target tokens to query tokens. All predictive signals are thereby forced through the BToks, converting the generative loss into dense, token-level supervision for semantic compression. At inference time, only the input and BToks are processed in a single forward pass with negligible overhead over conventional last-token pooling. On MMEB-V2 (78 datasets, 3 modalities, 9 meta-tasks), our approach achieves state-of-the-art among 2B-scale methods under comparable data conditions, attaining an Overall score of 59.0 (+3.6 over VLM2Vec-V2) with substantial gains on semantically demanding tasks (e.g., +12.6 on Video-QA).

Large language models (LLMs) owe much of their stellar performance to expansive input contexts, yet such verbosity inflates monetary costs, carbon footprint, and inference-time latency. Much of this overhead manifests from the redundant low-utility tokens present in typical prompts, as only a fraction of tokens typically carries the majority of the semantic weight. We address this inefficiency by introducing FrugalPrompt, a novel prompt compression framework for LLMs, which retains only the most semantically significant tokens. Leveraging two state-of-the-art token attribution methods, GlobEnc and DecompX, we assign salience scores to every token in an input sequence, rank them to preserve the top-k% tokens in their original order, and obtain a sparse frugalized prompt. We evaluate the approach across four NLP tasks: Sentiment Analysis, Commonsense QA, Summarization, and Mathematical Reasoning, using a suite of frontier LLMs. For the first three tasks, a 20% prompt reduction incurs only a marginal loss in task performance, demonstrating that contemporary LLMs can reconstruct elided context from high-salience cues. In contrast, performance on mathematical reasoning deteriorates sharply, reflecting a stronger dependence on complete token continuity. Further analysis with bottom-k% and random-k% tokens reveals asymmetric performance patterns that may suggest potential task contamination effects, wherein models may resort to shallow memorized patterns from pretraining exposure for conventional NLP tasks. We posit that our work contributes to a more nuanced understanding of LLM behavior in performance-efficiency trade-offs, and delineate the boundary between tasks tolerant to contextual sparsity and those requiring exhaustive context. Our source code and models are available at: https://github.com/Starscream-11813/Frugal-ICL.

Tokenization imposes a fixed granularity on the input text, freezing how a language model operates on data and how far in the future it predicts. Byte Pair Encoding (BPE) and similar schemes split text once, build a static vocabulary, and leave the model stuck with that choice. We relax this rigidity by introducing an autoregressive U-Net that learns to embed its own tokens as it trains. The network reads raw bytes, pools them into words, then pairs of words, then up to 4 words, giving it a multi-scale view of the sequence. At deeper stages, the model must predict further into the future -- anticipating the next few words rather than the next byte -- so deeper stages focus on broader semantic patterns while earlier stages handle fine details. When carefully tuning and controlling pretraining compute, shallow hierarchies tie strong BPE baselines, and deeper hierarchies have a promising trend. Because tokenization now lives inside the model, the same system can handle character-level tasks and carry knowledge across low-resource languages.

Tokenization is associated with many poorly understood shortcomings in language models (LMs), yet remains an important component for long sequence scaling purposes. This work studies how tokenization impacts model performance by analyzing and comparing the stochastic behavior of tokenized models with their byte-level, or token-free, counterparts. We discover that, even when the two models are statistically equivalent, their predictive distributions over the next byte can be substantially different, a phenomenon we term as "tokenization bias''. To fully characterize this phenomenon, we introduce the Byte-Token Representation Lemma, a framework that establishes a mapping between the learned token distribution and its equivalent byte-level distribution. From this result, we develop a next-byte sampling algorithm that eliminates tokenization bias without requiring further training or optimization. In other words, this enables zero-shot conversion of tokenized LMs into statistically equivalent token-free ones. We demonstrate its broad applicability with two use cases: fill-in-the-middle (FIM) tasks and model ensembles. In FIM tasks where input prompts may terminate mid-token, leading to out-of-distribution tokenization, our method mitigates performance degradation and achieves an approximately 18% improvement in FIM coding benchmarks, consistently outperforming the standard token healing fix. For model ensembles where each model employs a distinct vocabulary, our approach enables seamless integration, resulting in improved performance (up to 3.7%) over individual models across various standard baselines in reasoning, knowledge, and coding.

Generative recommender systems have recently attracted attention by formulating next-item prediction as an autoregressive sequence generation task. However, most existing methods optimize standard next-token likelihood and implicitly treat all tokens as equally informative, which is misaligned with semantic-ID-based generation. Accordingly, we propose two complementary information-gain-based token-weighting strategies tailored to generative recommendation with semantic IDs. Front-Greater Weighting captures conditional semantic information gain by prioritizing early tokens that most effectively reduce candidate-item uncertainty given their prefixes and encode coarse semantics. Frequency Weighting models marginal information gain under long-tailed item and token distributions, upweighting rare tokens to counteract popularity bias. Beyond individual strategies, we introduce a multi-target learning framework with curriculum learning that jointly optimizes the two token-weighted objectives alongside standard likelihood, enabling stable optimization and adaptive emphasis across training stages. Extensive experiments on benchmark datasets show that our method consistently outperforms strong baselines and existing token-weighting approaches, with improved robustness, strong generalization across different semantic-ID constructions, and substantial gains on both head and tail items. Code is available at https://github.com/CHIUWEINING/Token-Weighted-Multi-Target-Learning-for-Generative-Recommenders-with-Curriculum-Learning.

In this work, we present a naive initialization scheme for word vectors based on a dense, independent co-occurrence model and provide preliminary results that suggest it is competitive and warrants further investigation. Specifically, we demonstrate through information-theoretic minimum description length (MDL) probing that our model, EigenNoise, can approach the performance of empirically trained GloVe despite the lack of any pre-training data (in the case of EigenNoise). We present these preliminary results with interest to set the stage for further investigations into how this competitive initialization works without pre-training data, as well as to invite the exploration of more intelligent initialization schemes informed by the theory of harmonic linguistic structure. Our application of this theory likewise contributes a novel (and effective) interpretation of recent discoveries which have elucidated the underlying distributional information that linguistic representations capture from data and contrast distributions.

Retrieval-Augmented Generation (RAG) has become a standard approach for enhancing large language models (LLMs) with external knowledge, mitigating hallucinations, and improving factuality. However, existing systems rely on generating natural language queries at each hop and maintaining a strict architectural separation between retriever and generator, preventing them from leveraging the full representational capacity of the LLM. We propose LAnR (Latent Abstraction for RAG), a unified framework in which a single LLM jointly performs encoding, retrieval, and generation entirely within its own latent space. Rather than generating textual queries, LAnR produces dense retrieval vectors from the hidden states of a designated [PRED] token and uses them to match against encoded document representations from the same model. Furthermore, LAnR adaptively decides when sufficient evidence has been retrieved using a lightweight MLP control head over those same hidden states, eliminating both the separate retriever and explicit token-level stopping reasoning. This design is motivated by our empirical observation that answer token entropy reliably signals retrieval sufficiency. Extensive experiments on six QA benchmarks spanning single-hop and multi-hop settings demonstrate that LAnR outperforms existing RAG methods, while achieving improved inference efficiency through reduced number of retrieval calls and tighter model integration.

Large Language Models (LLMs) face computational inefficiencies and redundant processing when handling long context inputs, prompting a focus on compression techniques. While existing semantic vector-based compression methods achieve promising performance, these methods fail to account for the intrinsic information density variations between context chunks, instead allocating soft tokens uniformly across context chunks. This uniform distribution inevitably diminishes allocation to information-critical regions. To address this, we propose Dynamic Allocation of Soft Tokens (DAST), a simple yet effective method that leverages the LLM's intrinsic understanding of contextual relevance to guide compression. DAST combines perplexity-based local information with attention-driven global information to dynamically allocate soft tokens to the informative-rich chunks, enabling effective, context-aware compression. Experimental results across multiple benchmarks demonstrate that DAST surpasses state-of-the-art methods.

Large Language Models (LLMs) have exhibited exceptional performance across a spectrum of natural language processing tasks. However, their substantial sizes pose considerable challenges, particularly in computational demands and inference speed, due to their quadratic complexity. In this work, we have identified a key pattern: certain seemingly meaningless special tokens (i.e., separators) contribute disproportionately to attention scores compared to semantically meaningful tokens. This observation suggests that information of the segments between these separator tokens can be effectively condensed into the separator tokens themselves without significant information loss. Guided by this insight, we introduce SepLLM, a plug-and-play framework that accelerates inference by compressing these segments and eliminating redundant tokens. Additionally, we implement efficient kernels for training acceleration. Experimental results across training-free, training-from-scratch, and post-training settings demonstrate SepLLM's effectiveness. Notably, using the Llama-3-8B backbone, SepLLM achieves over 50% reduction in KV cache on the GSM8K-CoT benchmark while maintaining comparable performance. Furthermore, in streaming settings, SepLLM effectively processes sequences of up to 4 million tokens or more while maintaining consistent language modeling capabilities.

Token embeddings, a mapping from discrete lexical symbols to continuous vectors, are at the heart of any language model (LM). However, lexical symbol meanings can also be determined and even redefined by their structural role in a long context. In this paper, we ask: is it possible for a language model to be performant without any fixed token embeddings? Such a language model would have to rely entirely on the co-occurence and repetition of tokens in the context rather than the a priori identity of any token. To answer this, we study lexinvariantlanguage models that are invariant to lexical symbols and therefore do not need fixed token embeddings in practice. First, we prove that we can construct a lexinvariant LM to converge to the true language model at a uniform rate that is polynomial in terms of the context length, with a constant factor that is sublinear in the vocabulary size. Second, to build a lexinvariant LM, we simply encode tokens using random Gaussian vectors, such that each token maps to the same representation within each sequence but different representations across sequences. Empirically, we demonstrate that it can indeed attain perplexity comparable to that of a standard language model, given a sufficiently long context. We further explore two properties of the lexinvariant language models: First, given text generated from a substitution cipher of English, it implicitly implements Bayesian in-context deciphering and infers the mapping to the underlying real tokens with high accuracy. Second, it has on average 4X better accuracy over synthetic in-context reasoning tasks. Finally, we discuss regularizing standard language models towards lexinvariance and potential practical applications.

Autoregressive (AR) modeling, known for its next-token prediction paradigm, underpins state-of-the-art language and visual generative models. Traditionally, a ``token'' is treated as the smallest prediction unit, often a discrete symbol in language or a quantized patch in vision. However, the optimal token definition for 2D image structures remains an open question. Moreover, AR models suffer from exposure bias, where teacher forcing during training leads to error accumulation at inference. In this paper, we propose xAR, a generalized AR framework that extends the notion of a token to an entity X, which can represent an individual patch token, a cell (a ktimes k grouping of neighboring patches), a subsample (a non-local grouping of distant patches), a scale (coarse-to-fine resolution), or even a whole image. Additionally, we reformulate discrete token classification as continuous entity regression, leveraging flow-matching methods at each AR step. This approach conditions training on noisy entities instead of ground truth tokens, leading to Noisy Context Learning, which effectively alleviates exposure bias. As a result, xAR offers two key advantages: (1) it enables flexible prediction units that capture different contextual granularity and spatial structures, and (2) it mitigates exposure bias by avoiding reliance on teacher forcing. On ImageNet-256 generation benchmark, our base model, xAR-B (172M), outperforms DiT-XL/SiT-XL (675M) while achieving 20times faster inference. Meanwhile, xAR-H sets a new state-of-the-art with an FID of 1.24, running 2.2times faster than the previous best-performing model without relying on vision foundation modules (\eg, DINOv2) or advanced guidance interval sampling.

Speculative decoding accelerates large language model (LLM) inference by using a small draft model to propose candidate tokens that a larger target model verifies. A critical hyperparameter in this process is the speculation length γ, which determines how many tokens the draft model proposes per step. Nearly all existing systems use a fixed γ (typically 4), yet empirical evidence suggests that the optimal value varies across task types and, crucially, depends on the compression level applied to the target model. In this paper, we present SpecKV, a lightweight adaptive controller that selects γ per speculation step using signals extracted from the draft model itself. We profile speculative decoding across 4 task categories, 4 speculation lengths, and 3 compression levels (FP16, INT8, NF4), collecting 5,112 step-level records with per-step acceptance rates, draft entropy, and draft confidence. We demonstrate that the optimal γ shifts across compression regimes and that draft model confidence and entropy are strong predictors of acceptance rate (correlation approx 0.56). SpecKV uses a small MLP trained on these signals to maximize expected tokens per speculation step, achieving a 56.0% improvement over the fixed-γ=4 baseline with only 0.34 ms overhead per decision (<0.5% of step time). The improvement is statistically significant (p < 0.001, paired bootstrap test). We release all profiling data, trained models, and notebooks as open-source artifacts.

Tasks that require character-level reasoning, such as counting or locating characters within words, remain challenging for contemporary language models. A common conjecture is that language models' reliance on subword units, rather than characters, contributes to their struggles with character-level tasks, yet recent studies offer conflicting conclusions about the role of tokenization, leaving its impact unclear. To address this gap, we introduce CharBench, a comprehensive benchmark of character-level tasks that is two orders of magnitude larger than existing alternatives. We evaluate a diverse range of leading open-weight and proprietary models on CharBench and find that it presents a significant challenge to modern LLMs, with an average accuracy of 43.6% and 32.3% on some tasks. We present an in-depth analysis of how intrinsic properties of words and their segmentations into tokens correspond to model performance. For counting tasks, we find that tokenization properties are weakly correlated with correctness, while the length of the queried word and the actual character count play a more significant part. In contrast, for tasks requiring intra-word positional understanding, performance is negatively correlated with the length of the token containing the queried character, suggesting that longer tokens obscure character position information for LLMs. We encourage future work to build on the benchmark and evaluation methodology introduced here as tools for improving model performance on such tasks.

The increasing context window size in Large Language Models (LLMs), such as the GPT and LLaMA series, has improved their ability to tackle complex, long-text tasks, but at the cost of inference efficiency, particularly regarding memory and computational complexity. Existing methods, including selective token retention and window-based attention, improve efficiency but risk discarding important tokens needed for future text generation. In this paper, we propose an approach that enhances LLM efficiency without token loss by reducing the memory and computational load of less important tokens, rather than discarding them.We address two challenges: 1) investigating the distribution of important tokens in the context, discovering recent tokens are more important than distant tokens in context, and 2) optimizing resources for distant tokens by sharing attention scores across layers. The experiments show that our method saves 35% KV cache without compromising the performance.

We present Neural Attention Search (NAtS), a framework that automatically evaluates the importance of each token within a sequence and determines if the corresponding token can be dropped after several steps. This approach can efficiently reduce the KV cache sizes required by transformer-based models during inference and thus reduce inference costs. In this paper, we design a search space that contains three token types: (i) Global Tokens will be preserved and queried by all the following tokens. (ii) Local Tokens survive until the next global token appears. (iii) Sliding Window Tokens have an impact on the inference of a fixed size of the next following tokens. Similar to the One-Shot Neural Architecture Search approach, this token-type information can be learned jointly with the architecture weights via a learnable attention mask. Experiments on both training a new transformer from scratch and fine-tuning existing large language models show that NAtS can efficiently reduce the KV cache size required for the models while maintaining the models' performance.

Hallucinations in Large Language Model (LLM) outputs for Question Answering (QA) tasks can critically undermine their real-world reliability. This paper introduces a methodology for robust, one-shot hallucination detection, specifically designed for scenarios with limited data access, such as interacting with black-box LLM APIs that typically expose only a few top candidate log-probabilities per token. Our approach derives uncertainty indicators directly from these readily available log-probabilities generated during non-greedy decoding. We first derive an Entropy Production Rate (EPR) that offers baseline performance, later augmented with supervised learning. Our learned model leverages the entropic contributions of the accessible top-ranked tokens within a single generated sequence, without multiple re-runs per query. Evaluated across diverse QA datasets and multiple LLMs, this estimator significantly improves token-level hallucination detection over state-of-the-art methods. Crucially, high performance is demonstrated using only the typically small set of available log-probabilities (e.g., top-10 per token), confirming its practical efficiency and suitability for API-constrained deployments. This work provides a lightweight technique to enhance the trustworthiness of LLM responses, at the token level, after a single generation pass, for QA and Retrieval-Augmented Generation (RAG) systems. Our experiments confirmed the performance of our method against existing approaches on public dataset as well as for a financial framework analyzing annual company reports.

The success of autoregressive (AR) language models in text generation has inspired the computer vision community to adopt Large Language Models (LLMs) for image generation. However, considering the essential differences between text and image modalities, the design space of language models for image generation remains underexplored. We observe that image tokens exhibit greater randomness compared to text tokens, which presents challenges when training with token prediction. Nevertheless, AR models demonstrate their potential by effectively learning patterns even from a seemingly suboptimal optimization problem. Our analysis also reveals that while all models successfully grasp the importance of local information in image generation, smaller models struggle to capture the global context. In contrast, larger models showcase improved capabilities in this area, helping to explain the performance gains achieved when scaling up model size. We further elucidate the design space of language models for vision generation, including tokenizer choice, model choice, model scalability, vocabulary design, and sampling strategy through extensive comparative experiments. Our work is the first to analyze the optimization behavior of language models in vision generation, and we believe it can inspire more effective designs when applying LMs to other domains. Finally, our elucidated language model for image generation, termed as ELM, achieves state-of-the-art performance on the ImageNet 256*256 benchmark. The code is available at https://github.com/Pepperlll/LMforImageGeneration.git.

Recent years have witnessed the rapid advancements of large language models (LLMs) and their expanding applications, leading to soaring demands for computational resources. The widespread adoption of test-time scaling further aggravates the tension between model capability and resource consumption, highlighting the importance of inference efficiency. However, a unified metric that accurately reflects an LLM's efficiency across different model sizes and architectures remains absent. Motivated by the correlation between compression and intelligence, we introduce information capacity, a measure of model efficiency based on text compression performance relative to computational complexity. Larger models can predict the next token more accurately, achieving greater compression gains but at higher computational costs. Empirical evaluations on mainstream open-source models show that models of varying sizes within a series exhibit consistent information capacity. This metric enables a fair efficiency comparison across model series and accurate performance prediction within a model series. A distinctive feature of information capacity is that it incorporates tokenizer efficiency, which affects both input and output token counts but is often neglected in LLM evaluations. We assess the information capacity of 49 models on 5 heterogeneous datasets and observe consistent results on the influences of tokenizer efficiency, pretraining data, and the mixture-of-experts architecture.

Scaling laws in language modeling traditionally quantify training loss as a function of dataset size and model parameters, providing compute-optimal estimates but often neglecting the impact of data quality on model generalization. In this paper, we extend the conventional understanding of scaling law by offering a microscopic view of data quality within the original formulation -- effective training tokens -- which we posit to be a critical determinant of performance for parameter-constrained language models. Specifically, we formulate the proposed term of effective training tokens to be a combination of two readily-computed indicators of text: (i) text diversity and (ii) syntheticity as measured by a teacher model. We pretrained over 200 models of 25M to 1.5B parameters on a diverse set of sampled, synthetic data, and estimated the constants that relate text quality, model size, training tokens, and eight reasoning task accuracy scores. We demonstrated the estimated constants yield +0.83 Pearson correlation with true accuracies, and analyzed it in scenarios involving widely-used data techniques such as data sampling and synthesis which aim to improve data quality.

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving that truncation methods that discard tokens below some probability threshold (the most common type of truncation) can guarantee that all sampled tokens have nonzero true probability. However, thresholds are a coarse heuristic, and necessarily discard some tokens with nonzero true probability as well. In pursuit of a more precise sampling strategy, we show that we can leverage a known source of model errors, the softmax bottleneck, to prove that certain tokens have nonzero true probability, without relying on a threshold. Based on our findings, we develop an experimental truncation strategy and the present pilot studies demonstrating the promise of this type of algorithm. Our evaluations show that our method outperforms its threshold-based counterparts under automatic and human evaluation metrics for low-entropy (i.e., close to greedy) open-ended text generation. Our theoretical findings and pilot experiments provide both insight into why truncation sampling works, and make progress toward more expressive sampling algorithms that better surface the generative capabilities of large language models.

As Large Language Models (LLMs) achieve remarkable progress in language understanding and generation, their training efficiency has become a critical concern. Traditionally, LLMs are trained to predict the next token in a sequence. Despite the success of token-level training, it suffers from considerable computational costs due to the need to process an extensive number of tokens. To mitigate this issue, this paper introduces patch-level training for LLMs, which reduces the sequence length by compressing multiple tokens into a single patch. During patch-level training, we feed the language model shorter sequences of patches and train it to predict the next patch, thereby processing the majority of the training data at a significantly reduced computational cost. Following this, the model continues token-level training on the remaining training data to align with the inference mode. Experiments on a diverse range of models (370M-2.7B parameters) demonstrate that patch-level training can reduce overall computational costs to 0.5times, without compromising the model performance compared to token-level training. Source code: https://github.com/shaochenze/PatchTrain.

Retrieval-Augmented Generation (RAG) has emerged as the predominant paradigm for grounding Large Language Model outputs in factual knowledge, effectively mitigating hallucinations. However, conventional RAG systems operate under a "retrieve-always" assumption, querying vector databases for every input regardless of query complexity. This static approach incurs substantial computational overhead and inference latency, particularly problematic for high-throughput production deployments. We introduce L-RAG (Lazy Retrieval-Augmented Generation), an adaptive framework that implements hierarchical context management through entropy-based gating. L-RAG employs a two-tier architecture: queries are first processed with a compact document summary, and expensive chunk retrieval is triggered only when the model's predictive entropy exceeds a calibrated threshold, signaling genuine uncertainty. Through experiments on SQuAD 2.0 (N=500) using the Phi-2 model, we demonstrate that L-RAG provides a tunable accuracy-efficiency trade-off: at a conservative threshold (tau=0.5), L-RAG achieves 78.2% accuracy, matching Standard RAG (77.8%), with 8% retrieval reduction; at a balanced threshold (tau=1.0), retrieval reduction increases to 26% with modest accuracy trade-off (76.0%). Latency analysis shows that L-RAG saves 80-210ms per query when retrieval latency exceeds 500ms. Analysis of entropy distributions reveals statistically significant separation (p < 0.001) between correct predictions (H=1.72) and errors (H=2.20), validating entropy as a reliable uncertainty signal. L-RAG offers a practical, training-free approach toward more efficient RAG deployment, providing system architects with a configurable knob to balance accuracy and throughput requirements.

Despite the increasing prevalence of large language models (LLMs), we still have a limited understanding of how their representational spaces are structured. This limits our ability to interpret how and what they learn or relate them to learning in humans. We argue LLMs are best seen as an instance of lossy compression, where over training they learn by retaining only information in their training data relevant to their objective(s). We show pre-training results in models that are optimally compressed for next-sequence prediction, approaching the Information Bottleneck bound on compression. Across an array of open weights models, each compresses differently, likely due to differences in the data and training recipes used. However even across different families of LLMs the optimality of a model's compression, and the information present in it, can predict downstream performance on across a wide array of benchmarks, letting us directly link representational structure to actionable insights about model performance. In the general case the work presented here offers a unified Information-Theoretic framing for how these models learn that is deployable at scale.

The next-token prediction (NTP) objective has been foundational in the development of modern large language models (LLMs), driving advances in fluency and generalization. However, NTP operates at the token level, treating deviations from a single reference continuation as errors even when alternative continuations are equally plausible or semantically equivalent (e.g., ``mom'' vs. ``mother''). As a result, token-level loss can penalize valid abstractions, paraphrases, or conceptually correct reasoning paths, biasing models toward surface form rather than underlying meaning. This mismatch between the training signal and semantic correctness motivates learning objectives that operate over higher-level representations. We propose a shift from token-level to concept-level prediction, where concepts group multiple surface forms of the same idea (e.g., ``mom,'' ``mommy,'' ``mother'' rightarrow MOTHER). We introduce various methods for integrating conceptual supervision into LLM training and show that concept-aware models achieve lower perplexity, improved robustness under domain shift, and stronger performance than NTP-based models on diverse NLP benchmarks. This suggests concept-level supervision as an improved training signal that better aligns LLMs with human semantic abstractions.

Soft prompt tuning achieves superior performances across a wide range of few-shot tasks. However, the performances of prompt tuning can be highly sensitive to the initialization of the prompts. We also empirically observe that conventional prompt tuning methods cannot encode and learn sufficient task-relevant information from prompt tokens. In this work, we develop an information-theoretic framework that formulates soft prompt tuning as maximizing mutual information between prompts and other model parameters (or encoded representations). This novel view helps us to develop a more efficient, accurate and robust soft prompt tuning method InfoPrompt. With this framework, we develop two novel mutual information based loss functions, to (i) discover proper prompt initialization for the downstream tasks and learn sufficient task-relevant information from prompt tokens and (ii) encourage the output representation from the pretrained language model to be more aware of the task-relevant information captured in the learnt prompt. Extensive experiments validate that InfoPrompt can significantly accelerate the convergence of the prompt tuning and outperform traditional prompt tuning methods. Finally, we provide a formal theoretical result for showing to show that gradient descent type algorithm can be used to train our mutual information loss.

While there has been a large body of research attempting to circumvent tokenization for language modeling (Clark et al., 2022; Xue et al., 2022), the current consensus is that it is a necessary initial step for designing state-of-the-art performant language models. In this paper, we investigate tokenization from a theoretical point of view by studying the behavior of transformers on simple data generating processes. When trained on data drawn from certain simple k^{th}-order Markov processes for k > 1, transformers exhibit a surprising phenomenon - in the absence of tokenization, they empirically fail to learn the right distribution and predict characters according to a unigram model (Makkuva et al., 2024). With the addition of tokenization, however, we empirically observe that transformers break through this barrier and are able to model the probabilities of sequences drawn from the source near-optimally, achieving small cross-entropy loss. With this observation as starting point, we study the end-to-end cross-entropy loss achieved by transformers with and without tokenization. With the appropriate tokenization, we show that even the simplest unigram models (over tokens) learnt by transformers are able to model the probability of sequences drawn from k^{th}-order Markov sources near optimally. Our analysis provides a justification for the use of tokenization in practice through studying the behavior of transformers on Markovian data.

The quadratic complexity of attention remains the central bottleneck in long-context inference for large language models. Prior acceleration methods either sparsify the attention map with structured patterns or permanently evict tokens at specific layers, which can retain irrelevant tokens or rely on irreversible early decisions despite the layer-/head-wise dynamics of token importance. In this paper, we propose Token Sparse Attention, a lightweight and dynamic token-level sparsification mechanism that compresses per-head Q, K, V to a reduced token set during attention and then decompresses the output back to the original sequence, enabling token information to be reconsidered in subsequent layers. Furthermore, Token Sparse Attention exposes a new design point at the intersection of token selection and sparse attention. Our approach is fully compatible with dense attention implementations, including Flash Attention, and can be seamlessly composed with existing sparse attention kernels. Experimental results show that Token Sparse Attention consistently improves accuracy-latency trade-off, achieving up to times3.23 attention speedup at 128K context with less than 1% accuracy degradation. These results demonstrate that dynamic and interleaved token-level sparsification is a complementary and effective strategy for scalable long-context inference.

Modern language models rely on static vocabularies, fixed before pretraining, in contrast to the adaptive vocabulary acquisition observed in human language learning. To bridge this gap, we introduce vocabulary curriculum learning, an approach that improves pretraining efficiency with log-linear scaling gains relative to vocabulary size. Our method alternates between entropy-guided vocabulary expansion and model optimization, enabling models to learn transferable representations across diverse tokenization granularities. This approach naturally gives rise to an optimal computation allocation pattern: longer tokens capture predictable content, while shorter tokens focus on more complex, harder-to-predict contexts. Experiments on small-scale GPT models demonstrate improved scaling efficiency, reinforcing the effectiveness of dynamic tokenization. We release our code to support further research and plan to extend our experiments to larger models and diverse domains.

Fine tuning has been regarded as a de facto approach for adapting large language models (LLMs) to downstream tasks, but the high training memory consumption inherited from LLMs makes this process inefficient. Among existing memory efficient approaches, activation-related optimization has proven particularly effective, as activations consistently dominate overall memory consumption. Although prior arts offer various activation optimization strategies, their data-agnostic nature ultimately results in ineffective and unstable fine tuning. In this paper, we propose TokenSeek, a universal plugin solution for various transformer-based models through instance-aware token seeking and ditching, achieving significant fine-tuning memory savings (e.g., requiring only 14.8% of the memory on Llama3.2 1B) with on-par or even better performance. Furthermore, our interpretable token seeking process reveals the underlying reasons for its effectiveness, offering valuable insights for future research on token efficiency. Homepage: https://runjia.tech/iclr_tokenseek/

Large Language Models (LLMs) must continuously learn and update knowledge to remain effective in dynamic real-world environments. While Low-Rank Adaptation (LoRA) is widely used for such memory updates, existing studies mainly rely on qualitative downstream evaluations, leaving the quantitative capacity limits and underlying dynamics of exact parametric memory largely unexplored. To bridge this gap, we employ LoRA as a controlled memory capacity probe within the latent space to systematically quantify exact parametric memory. We introduce the Parametric Memory Law, a robust power law linking loss reduction Delta L to effective parameters and sequence length. At the token level, fine-grained analysis reveals a deterministic phase transition, demonstrating that a prediction probability of p > 0.5 constitutes a sufficient condition for verbatim recall under greedy decoding. Driven by these insights, we introduce MemFT, a threshold-guided optimization strategy that dynamically redistributes the training budget toward sub-threshold tokens. Empirical evaluations demonstrate that MemFT can enhance memory fidelity and efficiency. Code will be released at https://github.com/zjunlp/ParametricMemoryLaw.

We present methodology for using dynamic evaluation to improve neural sequence models. Models are adapted to recent history via a gradient descent based mechanism, causing them to assign higher probabilities to re-occurring sequential patterns. Dynamic evaluation outperforms existing adaptation approaches in our comparisons. Dynamic evaluation improves the state-of-the-art word-level perplexities on the Penn Treebank and WikiText-2 datasets to 51.1 and 44.3 respectively, and the state-of-the-art character-level cross-entropies on the text8 and Hutter Prize datasets to 1.19 bits/char and 1.08 bits/char respectively.